Elastic boundary wave device, resonator, and filter

ABSTRACT

An elastic boundary wave device includes a LiNbO 3  substrate, an electrode exciting an elastic wave and provided on the substrate, and a silicon oxide film provided on the substrate to cover the electrode, and parameters of the elastic boundary wave device have any one of ranges, where “θ” is a rotation Y cut angle of the substrate, “a” is a ratio of copper density with respect to a density of a material used as the electrode, “λ” is a wavelength of the elastic wave excited by the electrode, “h” is a film thickness of the electrode, “H” is a thickness of the silicon oxide film.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention generally relates to elastic boundary wave devices,resonators, and filters, and more particularly, to an elastic boundarywave device, resonator, and filter, in which Stoneley wave can besuppressed.

2. Description of the Related Art

There are known surface acoustic wave (hereinafter, referred to as SAW)devices, as one of the devices that utilize elastic waves. The SAWdevices are for use in various circuits such as, for example, transmitbandpass filter, receive bandpass filter, local filter, antennaduplexer, intermediate frequency (IF) filter, frequency modulation (FM)modulator, and the like. The circuits process wireless signals rangingfrom 45 MHz to 2 GHz of frequency bands typically used by, for example,mobile telephones.

In order to improve the temperature characteristics, Japanese PatentApplication Publication No. 2003-209458 (hereinafter, referred to asDocument 1) discloses an elastic surface wave device, in which there isdeposited on a piezoelectric substrate, a silicon oxide film having adifferent code in the temperature characteristic from the piezoelectricsubstrate. In an elastic surface wave device, elastic waves concentrateand propagate along the substrate surface. A foreign material adhered tothe substrate surface will change or degrade the characteristicsthereof, such as the change in frequency, increase in loss, or the like.For this reason, the elastic surface wave device is generally mounted onthe hermetically sealed package. This makes it difficult to reduce thesize of the device, leading to increased production cost.

Masatsune Yamaguchi, Takashi Yamashita, Ken-ya Hashimoto, Tatsuya Omori,“Highly Piezoelectric Boundary Waves in Si/SiO₂/LiNbO₃ Structure”Proceeding of 1998 IEEE International Frequency Control Symposium (U.S.)IEEE, 1998, p.p. 484-488 (hereinafter, referred to as Document 2)discloses a device that utilizes boundary waves propagating along theboundary between different mediums, instead of the surface waves, inorder to improve the temperature characteristic and to reduce the sizeand production cost of the device. Document 2 discloses the boundarywaves in the structure where a silicon oxide film and a silicon film aredeposited on a 0-degree rotation Y-plate LiNbO₃ (LN substrate), on thebasis of the calculation results.

It is to be noted that Document 2 does not describe a method forproducing an elastic boundary wave device having excellentcharacteristics suitable for practical use. As a problem against thepractical use, there is an elastic wave excited as an unnecessaryresponse, other than the elastic boundary waves utilized in the elasticboundary wave device. Such unnecessary response degrades the excellentfrequency characteristics of the elastic boundary waves serving as afunction of the elastic boundary wave device. As an example, FIG. 1shows passband characteristics of a one-port resonator with an elasticboundary wave device. SH of FIG. 1 represents a response of a wavehaving a main component of Shear Horizontal (SH) wave utilized in theelastic boundary wave device. In other words, SH wave is used to fulfillthe function thereof in the elastic boundary waved device. SV of FIG. 1is observed as a response at a lower frequency side of SH. This iscalled Stoneley wave having a main component of Shear Vertical (SV)wave. As shown in FIG. 1, the Stoneley wave exciting as an elasticboundary wave is present at the closest frequency of the boundary wavehaving a main component of SH wave utilized in the elastic boundary wavedevice.

SUMMARY OF THE INVENTION

The present invention has been made in view of the above circumstancesand provides an elastic boundary wave device, resonator, and filter, inwhich Stoneley wave can be suppressed, the Stoneley wave being presentat the closest frequency of the boundary waves utilized as a function ofthe elastic boundary wave device.

According to one aspect of the present invention, there is provided anelastic boundary wave device including: a LiNbO₃ substrate; an electrodeexciting an elastic wave and provided on the substrate; and a siliconoxide film provided on the substrate to cover the electrode, andparameters of the elastic boundary wave device have any one of rangesbelow, where “θ” is a rotation Y cut angle of the substrate, “a” is aratio of copper density with respect to a density of a material used asthe electrode, “λ” is a wavelength of the elastic wave excited by theelectrode, “h” is a film thickness of the electrode, “H” is a thicknessof the silicon oxide film:

when 0.045λ/a≦h<0.0525λ/a, and

when 25°≦θ<26.5°, 0.39λ≦H<0.46λ,

when 26.5°≦θ<27.5°, 0.41λ≦H<0.48λ,

when 27.5°≦θ<28.5°, 0.42λ≦H<0.51λ,

when 28.5°≦θ<29.5°, 0.43λ≦H<0.53λ,

when 29.5°≦θ<30.5°, 0.45λ≦H<0.56λ,

when 30.5°≦θ<31.5°, 0.46λ≦H<0.58λ,

when 31.5°≦θ<32.5°, 0.47λ≦H<0.61λ,

when 32.5°≦θ<33.5°, 0.48λ≦H<0.64λ,

when 33.5°≦θ<35°, 0.48λ≦H<0.67λ,

when 35°≦θ<37.5°, 0.5λ≦H<0.74λ,

when 37.5°≦θ<42°, 0.52λ≦H<0.8λ,

when 42°≦θ<57°, 0.55λ≦H<0.8λ,

when 57°≦θ<63°, 0.51λ≦H<0.8λ,

when 63°≦θ<69°, 0.46λ≦H<0.8λ,

when 69°≦θ<75°, 0.39λ≦H<0.8λ,

when 75°≦θ<99°, 0.3λ≦H<0.8λ, and

when 99°≦θ<105°, 0.58λ≦H<0.8λ,

when 0.0525λ/a≦h<0.065λ/a and

when 24°≦θ<25°, 0.3λ≦H<0.32λ,

when 25°≦θ<26.5°, 0.3λ≦H<0.37λ,

when 26.5°≦θ<27.5°, 0.33λ≦H<0.38λ,

when 27.5°≦θ<28.5°, 0.34λ≦H<0.41λ,

when 28.5°≦θ<29.5°, 0.37λ≦H<0.43λ,

when 29.5°≦θ<30.5°, 0.39λ≦H<0.44λ,

when 30.5°≦θ<31.5°, 0.42λ≦H<0.47λ,

when 31.5°≦θ<32.5°, 0.44λ≦H<0.48λ,

when 32.5°≦θ<33.5°, 0.47λ≦H<0.49λ,

when 33.5°≦θ<34.5°, 0.47λ≦H<0.51λ,

when 34.5°≦θ<35.5°, 0.48λ≦H<0.57λ,

when 35.5°≦θ<36.5°, 0.5λ≦H<0.62λ,

when 36.5°≦θ<38°, 0.52λ≦H<0.67λ,

when 38°≦θ<40.5°, 0.54λ≦H<0.79λ,

when 40.5°≦θ<43.5°, 0.58λ≦H<0.8λ,

when 43.5°≦θ<46.5°, 0.61λ≦H<0.8λ,

when 46.5°≦θ<51°, 0.64λ≦H<0.8λ,

when 51°≦θ<57°, 0.69λ≦H<0.8λ, and

when 57°≦θ<63°, 0.78λ≦H<0.8λ,

when 0.065λ/a≦h<0.0725λ/a and

when 25.5°≦θ<26.5°, 0.3λ≦H<0.32λ,

when 26.5°≦θ<27.5°, 0.3λ≦H<0.36λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.38λ,

when 28.5°≦θ<29.5°, 0.32λ≦H<0.43λ,

when 29.5°≦θ<30.5°, 0.34λ≦H<0.46λ,

when 30.5°≦θ<31.5°, 0.36λ≦H<0.5λ,

when 31.5°≦θ<32.5°, 0.39λ≦H<0.55λ,

when 32.5°≦θ<33.5°, 0.43λ≦H<0.6λ,

when 33.5°≦θ<35°, 0.46λ≦H<0.66λ,

when 35°≦θ<36.5°, 0.54λ≦H<0.8λ,

when 36.5°≦θ<37.5°, 0.59λ≦H<0.8λ,

when 37.5°≦θ<38.5°, 0.65λ≦H<0.8λ, and

when 38.5°≦θ<39°, 0.73λ≦H<0.8λ,

when 0.0725λ/a≦h<0.0775λ/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.35λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.39λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.43λ,

when 29.5°≦θ<30.5°, 0.33λ≦H<0.49λ,

when 30.5°≦θ<31.5°, 0.35λ≦H<0.56λ,

when 31.5°≦θ<32.5°, 0.39λ≦H<0.63λ,

when 32.5°≦θ<33.5°, 0.43λ≦H<0.75λ,

when 33.5°≦θ<34.5°, 0.47λ≦H<0.8λ,

when 34.5°≦θ<35.5°, 0.52λ≦H<0.8λ,

when 35.5°≦θ<36.5°, 0.57λ≦H<0.8λ,

when 36.5°≦θ<37.5°, 0.63λ≦H<0.8λ, and

when 37.5°≦θ<38.5°, 0.72λ≦H<0.8λ,

when 0.0775λ/a≦h<0.0825λ/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.34λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.41λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.47λ,

when 29.5°≦θ<30.5°, 0.32λ≦H<0.56λ,

when 30.5°≦θ<31.5°, 0.36λ≦H<0.69λ,

when 31.5°≦θ<32.5°, 0.39λ≦H<0.8λ,

when 32.5°≦θ<33.5°, 0.44λ≦H<0.8λ,

when 33.5°≦θ<35°, 0.5λ≦H<0.8λ,

when 35°≦θ<36.5°, 0.65λ≦H<0.8λ, and

when 36.5°≦θ<38°, 0.77λ≦H<0.8λ,

when 0.0825λ/a≦h<0.0875λ/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.36λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.44λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.57λ,

when 29.5°≦θ<30.5°, 0.32λ≦H<0.8λ,

when 30.5°≦θ<31.5°, 0.37λ≦H<0.8λ,

when 31.5°≦θ<32.5°, 0.43λ≦H<0.8λ,

when 32.5°≦θ<33.5°, 0.51λ≦H<0.8λ,

when 33.5°≦θ<34.5°, 0.59λ≦H<0.8λ, and

when 34.5°≦θ<35.5°, 0.72λ≦H<0.8 λ.

when 0.0875λ/a≦h<0.0925λ/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.39λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.58λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.8λ,

when 29.5°≦θ<30.5°, 0.33λ≦H<0.8λ,

when 30.5°≦θ<31.5°, 0.43λ≦H<0.8λ,

when 31.5°≦θ<32.5°, 0.53λ≦H<0.8λ, and

when 32.5°≦θ<33.5°, 0.67λ≦H<0.8,

when 0.0925λ/a≦h<0.0975λ/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.63λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.8λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.8λ,

when 29.5°≦θ<30.5°, 0.42λ≦H<0.8λ, and

when 30.5°≦θ<31.5°, 0.6λ≦H<0.8λ,

when 0.0975λ/a≦h<0.1025λ/a and

when 25.5°≦θ<26.5°, 0.32λ≦H<0.7λ,

when 26.5°≦θ<27.5°, 0.3λ≦H<0.8λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.8λ, and

when 28.5°≦θ<29.5°, 0.45λ≦H<0.8λ,

when 0.1025λ/a≦h<0.1125λ/a and

when 24.5°≦θ<25.5°, 0.6λ≦H<0.8λ,

when 25.5°≦θ<26.5°, 0.3λ≦H<0.8λ,

when 26.5°≦θ<27.5°, 0.3λ≦H<0.8λ, and

when 27.5°≦θ<28.5°, 0.3λ≦H<0.33λ and

0.64λ≦H<0.8λ, and

when 0.1125λ/a≦h<0.12λ/a and

when 22.5°≦θ<23.5°, 0.47λ≦H<0.76λ, and

when 23.5°≦θ<24.5°, 0.36λ≦H<0.45 λ.

According to another aspect of the present invention, there is providedan elastic boundary wave device including: a LiNbO₃ substrate; anelectrode exciting an elastic wave and provided on the substrate; and asilicon oxide film provided on the substrate to cover the electrode, andparameters of the elastic boundary wave device have any one of rangesbelow, where “θ” is a rotation Y cut angle of the substrate, “a” is aratio of copper density with respect to a density of a material used asthe electrode, “λ” is a wavelength of the elastic wave excited by theelectrode, “h” is a film thickness of the electrode, “H” is a thicknessof the silicon oxide film:

when 0°≦θ<0.5° and

when 0.6≦H/λ≦0.8, h/(λ·a)≦H/λ, and additionally,

when 0.6≦H/λ<0.625, h/(λ·a)≧−2H/λ+1.8, and

when 0.625≦H/λ≦0.8, h/(λ·a)≧1.543 (H/λ)²−2.484H/λ+1.5,

when 0.5°≦θ<2° and

when 0.508≦H/λ≦0.8, h/(λ·a)≦H/λ, and additionally,

when 0.508≦H/λ<0.531, h/(λ·a)≧−0.3478 H/λ+0.6847,

when 0.531≦H/λ<0.6, h/(λ·)≧−0.6087 H/λ+0.8232, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧0.6 (H/λ)²−0.98 H/λ+0.83,

when 2°≦θ<4.5° and

when 0.45≦H/λ≦0.8, h/(λ·a)≦H/λ, and additionally,

when 0.45≦H/λ<0.5, h/(λ·a)≧28.998 (H/λ)²−29.088 H/λ+7.668,

when 0.5≦H/λ<0.65, h/(λ·a)≧1.6 (H/λ)²−2.06 H/λ+1.003, and

when 0.65≦H/λ≦0.8, h/(λ·a)≧−0.0733H/λ+0.3877,

when 4.5°≦θ<7.5° and

when 0.3625≦H/λ<0.496, h/(λ·a)<H/λ,

when 0.496≦H/λ<0.55, h/(λ·a)≦−0.111 H/λ+0.5511,

when 0.55≦H/λ<0.65, h/(λ·a)≦3.4 (H/λ)²−4.45 H/λ+1.909,

when 0.65≦H/λ<0.7, h/(λ·a)≦−0.06H/λ+0.492, and

when 0.7≦H/λ≦0.8, h/(λ·a)≦0.45, and additionally,

when 0.3625≦H/λ<0.3875, h/(λ·a)≧−0.46 H/λ+0.5293,

when 0.3875≦H/λ<0.4, h/(λ·a)≧−2.96 H/λ+1.498,

when 0.4≦H/λ<0.45, h/(λ·a)≧−0.58H/λ+0.546,

when 0.45≦H/λ<0.6, h/(λ·a)≧1.2667 (H/λ)²−1.503 H/λ+0.705, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧−0.04 H/λ+0.283,

when 7.5°≦θ<9.5° and

when 0.315≦H/λ<0.406, h/(λ·a)≦H/λ,

when 0.406≦H/λ<0.419, h/(λ·a)≦−1.077H/λ+0.8432,

when 0.419≦H/λ<0.45, h/(λ·a)≦61.7512 (H/λ)²−55.565 H/λ+12.8326,

when 0.45≦H/λ<0.6, h/(λ·a)≦1.8667 (H/λ)²−2.233 H/λ+0.96, and

when 0.6≦H/λ≦0.8, h/(λ·a)≦0.2 (H/λ)²−0.32 H/λ+0.412, and additionally,

when 0.315≦H/λ≦0.342, h/(λ·a)≧−0.5556 H/λ+0.49,

when 0.342≦H/λ<0.35, h/(λ·a)≧−3.75 H/λ+1.5825,

when 0.35≦H/λ<0.4, h/(λ·a)≧−0.6 H/λ+0.48,

when 0.4≦H/λ<0.55, h/(λ·a)≧1.133 (H/λ)²−1.243 H/λ+0.556, and

when 0.55≦H/λ≦0.8, h/(λ·a)≧0.1067 (H/λ)²−0.18 H/λ+0.2817,

when 9.5°≦θ≦10.5° and

when 0.31≦H/λ<0.37, h/(λ·a)≦H/λ,

when 0.37≦H/λ<0.383, h/(λ·a)≦0.37,

when 0.383≦H/λ<0.392, h/(λ·a)≦−1.111 H/λ+0.7956,

when 0.392≦H/λ<0.4, h/(λ·a)≦−2.5 H/λ+1.34,

when 0.4≦H/λ<0.45, h/(λ·)−12 (H/λ)²−11.1 H/λ+2.86,

when 0.45≦H/λ<0.5, h/(λ·a)≦3.2 (H/λ)²−3.36 H/λ+1.159,

when 0.5≦H/λ<0.61, h/(λ·a)≦0.5455 (H/λ)²−0.7327H/λ+0.509, and

when 0.61≦H/λ≦0.8, h/(λ·a)≦0.08848 (H/λ)²−0.1616 H/λ+0.3307, andadditionally,

when 0.31≦H/λ<0.331, h/(λ·a)≧−0.4762 H/λ+0.4576,

when 0.331≦H/λ<0.35, h/(λ·a)≧−2.632 H/λ+1.171,

when 0.35≦H/λ<0.4, h/(λ·a)≧−0.5 H/λ+0.425,

when 0.4≦H/λ<0.5, h/(λ·a)≧(H/λ)²−1.09 H/λ+0.501, and

when 0.5≦H/λ≦0.8, h/(λ·a)≧0.1 (H/λ)²−0.17 H/λ+0.266,

when 10.5°≦θ<11.5° and

when 0.304≦H/λ<0.36, h/(λ·a)≦H/λ,

when 0.36≦H/λ<0.3625, h/(λ·a)≦−4 H/λ+1.8,

when 0.3625≦H/λ<0.375, h/(λ·a)<−0.8 H/λ+0.64,

when 0.375≦H/λ<0.4, h/(λ·a)≦80.702 (H/λ)²−64.344 H/λ+13.120,

when 0.4≦H/λ<0.5, h/(λ·a)≦3 (H/λ)²−3.091 H/λ+1.051,

when 0.5≦H/λ<0.7, h/(λ·a)≦0.4 (H/λ)²−0.56 H/λ+0.436, and

when 0.7≦H/λ<0.8, h/(λ·a)≦0.02 H/λ+0.254, and additionally,

when 0.304≦H/λ≦0.329, h/(λ·a)≧−0.56 H/λ+0.474,

when 0.329≦H/λ<0.331, h/(λ·a)≧15 H/λ+5.225,

when 0.331≦H/λ<0.35, h/(λ·a)≧−1.579 H/λ+0.7826,

when 0.35≦H/λ<0.4, h/(λ·a)≧−0.4 H/λ+0.37,

when 0.4≦H/λ<0.575, h/(λ·a)≧0.4762 (H/λ)²−0.5786 H/λ+0.3652, and

when 0.575≦H/λ≦0.8, h/(λ·a)≧0.0381 (H/λ)²−0.07905 H/λ+0.2229,

when 11.5°≦θ≦12.5°, and

when 0.3≦H/λ<0.35, h/(λ·a)≦H/λ,

when 0.35≦H/λ<0.358, h/(λ·a)≦−1.25H/λ+0.7875,

when 0.358≦H/λ<0.3625, h/(λ·a)<−6.667H/λ+2.7267,

when 0.3625≦H/λ<0.4, h/(λ·a)≦27.781 (H/λ)²−22.3379H/λ+4.7569,

when 0.4≦H/λ<0.5, h/(λ·a)≦2.18 (H/λ)²−2.271 H/λ+0.8263,

when 0.5≦H/λ<0.65, h/(λ·a)≦0.44 (H/λ)²−0.578 H/λ+0.4148, and

when 0.65≦H/λ≦0.8, h/(λ·a)≦−0.02667H/λ+0.2423, and additionally,

when 0.3≦H/λ<0.308, h/(λ·a)≧−0.5 H/λ+0.45,

when 0.308≦H/λ<0.35, h/(λ·a)≧25.1541 (H/λ)²−18.099 H/λ+3.4683,

when 0.35≦H/λ<0.45, h/(λ·a)≧1.8 (H/λ)²−1.69H/λ+0.586,

when 0.45≦H/λ<0.6, h/(λ·a)≧0.3333 (H/λ)²−0.4167H/λ+0.31, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧−0.02H/λ+0.192,

when 12.5°≦θ<13.5° and

when 0.3≦H/λ<0.32, h/(λ·a)≦H/λ,

when 0.32≦H/λ<0.35, h/(λ·a)≦−H/λ+0.64,

when 0.35≦H/λ<0.373, h/(λ·a)<−1.3044 H/λ+0.7465,

when 0.373≦H/λ<0.4, h/(λ·a)≦−0.6296H/λ+0.4949,

when 0.4≦H/λ<0.5, h/(λ·a)≦1.6 (H/λ)²−1.66 H/λ+0.651,

when 0.5≦H/λ<0.65, h/(λ·)≦0.4667 (H/λ)²−0.61 H/λ+0.4093, and

when 0.65≦H/λ≦0.8, h/(λ·a)≦−0.02H/λ+0.223, and additionally,

when 0.3≦H/λ<0.35, h/(λ·a)≧−0.8 H/λ+0.48,

when 0.35≦H/λ<0.45, h/(λ·a)≧−0.2H/λ+0.27,

when 0.45≦H/λ<0.625, h/(λ·a)≧0.09524 (H/λ)²−0.1595 H/λ+0.2325, and

when 0.65≦H/λ<0.8, h/(λ·a)≧−0.01143H/λ+0.1771,

when 13.5°≦θ<14.5° and

when 0.3≦H/λ<0.318, h/(λ·a)<H/λ,

when 0.318≦H/λ<0.325, h/(λ·a)≦−4 H/λ+1.59,

when 0.325≦H/λ<0.4, h/(λ·a)≦6.933 (H/λ)²−5.88 H/λ+1.4687,

when 0.4≦H/λ<0.585, h/(λ·a)≦0.6618 (H/λ)²−0.7924 H/λ+0.437, and

when 0.585≦H/λ<0.8, h/(λ·a)≦0.11527 (H/λ)²−0.1829 H/λ+0.2676, andadditionally,

when 0.3≦H/λ<0.35, h/(λ·a)≧−0.6 H/λ+0.4,

when 0.35≦H/λ<0.475, h/(λ·a)≧0.8 (H/λ)²−0.82 H/λ+0.379,

when 0.475≦H/λ<0.65, h/(λ·a)≧0.2095 (H/λ)²−0.2814 H/λ+0.2564, and

when 0.65≦H/λ≦0.8, h/(λ·a)≧0.0133 H/λ+0.1707,

when 14.5°≦θ≦15.5° and

when 0.3≦H/λ<0.304, h/(λ·a)≦H/λ,

when 0.304≦H/λ<0.308, h/(λ·a)≦−1.25 H/λ+0.685,

when 0.308≦H/λ<0.321, h/(λ·a)≦−2.308 H/λ+1.011,

when 0.321≦H/λ<0.375, h/(λ·a)≦11.239 (H/λ)²−8.748 H/λ+1.920,

when 0.375≦H/λ<0.5, h/(λ·a)≦1.1733 (H/λ)²−1.2347 H/λ+0.518,

when 0.5≦H/λ<0.65, h/(λ·a)≦0.267 (H/λ)²−0.36 H/λ+0.3073, and

when 0.65≦H/λ≦0.8, h/(λ·a)≦−0.01333 H/λ+0.1947, and additionally,

when 0.3≦H/λ<0.35, h/(λ·a)≧−0.5 H/λ+0.355,

when 0.35≦H/λ<0.4, h/(λ·a)≧−0.2 H/λ+0.25,

when 0.4≦H/λ<0.5, h/(λ·a)≧−0.1H/λ+0.21,

when 0.5≦H/λ<0.7, h/(λ·a)≧−0.03 H/λ+0.175, and

when 0.7≦H/λ≦0.8, h/(λ·a)≧0.154,

when 15.5°≦θ<16.5° and

when 0.3≦H/λ<0.308, h/(λ·a)≦−1.25H/λ+0.675,

when 0.308≦H/λ<0.311, h/(λ·a)≦−10H/λ+3.37,

when 0.311≦H/λ<0.321, h/(λ·a)≦−2H/λ+0.882,

when 0.321≦H/λ<0.4, h/(λ·a)≦5.9188 (H/λ)²−4.799 H/λ+1.171,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.711 (H/λ)²−0.7956 H/λ+0.4024,

when 0.55≦H/λ≦0.8, h/(λ·a)≦0.128 (H/λ)²−0.197 H/λ+0.2495, andadditionally,

when 0.3≦H/λ<0.35, h/(λ·a)≧−0.4 H/λ+0.31,

when 0.35≦H/λ<0.5, h/(λ·a)≧0.3556 (H/λ)²−0.4089H/λ+0.2696, and

when 0.5≦H/λ≦0.8, h/(λ·a)≧0.08762 (H/λ)²−0.1306 H/λ+0.1974,

when 16.5°≦θ<17.5° and

when 0.3≦H/λ<0.4, h/(λ·a)<8.6 (H/λ)²−6.75 H/λ+1.511,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.467 (H/λ)²−0.557H/λ+0.335, and

when 0.55≦H/λ≦0.8, h/(λ·a)≦0.0667 (H/λ)²−0.11 H/λ+0.2103, andadditionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧1.133 (H/λ)²−1.043 H/λ+0.391,

when 0.45≦H/λ<0.6, h/(λ·a)≧0.133 (H/λ)²−0.183 H/λ+0.2065, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧−0.0075 H/λ+0.149,

when 17.5°≦θ<18.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦4 (H/λ)²−3.28 H/λ+0.848,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.467 (H/λ)²−0.537 H/λ+0.316, and

when 0.55≦H/λ≦0.8, h/(λ·a)≦0.1 (H/λ)²−0.155 H/λ+0.217, and additionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧0.867 (H/λ)²−0.817 H/λ+0.337,

when 0.45≦H/λ<0.55, h/(λ·a)≧−0.05 H/λ+0.1675, and

when 0.55≦H/λ≦0.8, h/(λ·a)≧−0.008 H/λ+0.1444,

when 18.5°≦θ<19.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦2.8 (H/λ)²−2.34 H/λ+0.655,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.467 (H/λ)²−0.537 H/λ+0.307, and

when 0.55≦H/λ≦0.8, h/(λ·a)≦0.04 (H/λ)²−0.07 H/λ+0.1794, andadditionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧0.933 (H/λ)²−0.847 H/λ+0.331, and

when 0.45≦H/λ<0.6, h/(λ·a)≧0.081 (H/λ)²−0.118 H/λ+0.1759, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧−0.005 H/λ+0.137,

when 19.5°≦θ<20.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦2.4 (H/λ)²−2 H/λ+0.574,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.4 (H/λ)²−0.46 H/λ+0.278, and

when 0.55≦H/λ≦−0.8, h/(λ·a)≦0.0933 (H/λ)²−0.142 H/λ+0.1959, andadditionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧0.667 (H/λ)²−0.627 H/λ+0.281, and

when 0.45≦H/λ<0.575, h/(λ·a)≧0.107 (H/λ)²−0.141 H/λ+0.176, and

when 0.575≦H/λ≦0.8, h/(λ·a)≧−0.00444 H/λ+0.1326,

when 20.5°≦θ<21.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦2.2 (H/λ)²−1.83 H/λ+0.529,

when 0.4≦H/λ<0.52, h/(λ·a)≦0.357 (H/λ)²−0.404 H/λ+0.2533, and

when 0.52≦H/λ≦0.8, h/(λ·a)≦0.0604 (H/λ)²−0.0976 H/λ+0.1744, andadditionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧0.733 (H/λ)²−0.657 H/λ+0.276, and

when 0.45≦H/λ≦0.8, h/(λ·a)≧0.04286 (H/λ)²−0.065 H/λ+0.1496,

when 21.5°≦θ<22.5° and

when 0.3≦H/λ<0.8, h/(λ·a)≦0.198 (H/λ)²−0.291 H/λ+0.234, andadditionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧0.8 (H/λ)²−0.69 H/λ+0.2735, and

when 0.45≦H/λ≦0.8, h/(λ·a)≧−0.00286 H/λ+0.1263,

when 22.5°≦θ<23.5° and

when 0.3≦H/λ<0.7, h/(λ·a)≦0.568 (H/λ)²−0.649 H/λ+0.2976, and

when 0.7≦H/λ<0.75, h/(λ·a)≦−0.03H/λ+0.1425, and additionally,

when 0.3≦H/λ≦0.73, h/(λ·a)≧0.136 (H/λ)²−0.174 H/λ+0.1719, and

when 0.73≦H/λ≦0.75, h/(λ·a)≧0.125 H/λ+0.02625,

when 23.5°≦θ<24° and

when 0.3≦H/λ<0.5, h/(λ·a)≦0.4 (H/λ)²−0.46 H/λ+0.246, and

when 0.5≦H/λ≦0.8, h/(λ·a)≦0.116, and additionally,

when 0.3≦H/λ<0.5, h/(λ·a)≧0.667 (H/λ)²−0.613 H/λ+0.253, and

when 0.5≦H/λ≦0.8, h/(λ·a)≧−0.01 H/λ+0.118, or

when 23.5°≦θ<24° and

when 0.3≦H/λ≦0.42, h/(λ·a)≦−0.208 H/λ+0.128, and additionally,

when 0.3≦H/λ≦0.42, h/(λ·a)≧−0.125 H/λ+0.0925.

According to yet another aspect of the present invention, there isprovided an elastic boundary wave device including: a LiNbO₃ substrate;an electrode exciting an elastic wave and provided on the substrate; anda silicon oxide film provided on the substrate to cover the electrode,and parameters of the elastic boundary wave device have any one ofranges below, where “θ” is a rotation Y cut angle of the substrate, “a”is a ratio of copper density with respect to a density of a materialused as the electrode, “λ” is a wavelength of the elastic wave excitedby the electrode, “h” is a film thickness of the electrode, “H” is athickness of the silicon oxide film:

when 0.03λ/a≦h<0.0375λ/a and

when 0.3≦H/λ≦0.8, θ≦75 (H/λ)²−82.5 H/λ+103.687, and additionally,

when 0.3≦H/λ<0.65, θ≦−85.7 H/λ+97.7, and

when 0.65≦H/λ≦0.8, θ≧42, or

when 0.03λ/a≦h<0.0375λ/a and

when 0.45≦H/λ<0.65, θ≦120H/λ−36, and

when 0.65≦H/λ≦0.8, θ≦42, and additionally,

when 0.45≦H/λ<0.5, θ≧18, and

when 0.5≦H/λ≦0.8, θ≧40H/λ−2,

when 0.0375λ/a≦h<0.0525λ/a and

when 0.3≦H/λ≦0.8, θ≦24 H/λ+88.8, and additionally,

when 0.3≦H/λ<0.55, θ≧−120 H/λ+114, and

when 0.55≦H/λ≦0.8, θ≧48, or

when 0.0375λ/a≦h<0.0525λ/a and

when 0.43≦H/λ<0.55, θ≦180 H/λ−51, and

when 0.55≦H/λ≦0.8, θ≦48, and additionally,

when 0.43≦H/λ≦0.8, θ≧34.3 H/λ+11.6,

when 0.0525λ/a≦h<0.065λ/a and

when 0.45≦H/λ≦0.8, θ<80 H/λ−4, and additionally,

when 0.45≦H/λ≦0.8, θ≧20 H/λ+23,

when 0.065λ/a≦h<0.0725λ/a and

when 0.3≦H/λ<0.7, θ≦−26.7 (H/λ)²+52 H/λ+15.5, and

when 0.7≦H/λ<0.8, θ≦25 H/λ+21, and additionally,

when 0.3≦H/λ≦0.8, θ≧−16.7 (H/λ)²+38.3 H/λ+16,

when 0.0725λ/a≦h<0.0775λ/a and

when 0.3≦H/λ≦0.8, θ≦−25 (H/λ)²+47.5 H/λ+17, and additionally,

when 0.3≦H/λ≦0.8, θ≧−25 (H/λ)²+42.5 H/λ+15.2,

when 0.0775λ/a≦h<0.0825λ/a and

when 0.3≦H/λ≦0.8, θ≦−21.4 (H/λ)²+38.2H/λ+20.1, and additionally,

when 0.3≦H/λ≦0.8, θ≧−23.3 (H/λ)²+35.8 H/λ+17.4,

when 0.0825λ/a≦h<0.0875λ/a and

when 0.3≦H/λ≦0.8, θ≦−13.3(H/λ)²+24.7 H/λ+24, and additionally,

when 0.3≦H/λ≦0.8, θ≧16 (H/λ)²+25.6 H/λ+19.8,

when 0.0875λ/a≦h<0.0925λ/a, and

when 0.3≦H/λ<0.55, θ≦10 H/λ+26.5, and

when 0.55≦H/λ≦0.8, θ≦6 H/λ+28.7, and additionally,

when 0.3≦H/λ≦0.8, θ≧4 H/λ+25.3,

when 0.0925λ/a≦h<0.0975λ/a and

when 0.3≦H/λ≦0.8, θ≦4 H/λ+28.3, and additionally,

when 0.3≦H/λ≦0.8, θ≧2 H/λ+25.9,

when 0.0975λ/a≦h<0.1025λ/a and

when 0.3≦H/λ≦0.8, θ≦2 H/λ+28.2, and additionally,

when 0.3≦H/λ≦0.8, θ≧26, and

when 0.1025λ/a≦h<0.105λ/a and

when 0.3≦H/λ≦0.8, θ≦28, and additionally,

when 0.3≦H/λ<0.5, θ≧−5 H/λ+27.5, and

when 0.5≦H/λ≦0.8, θ≧25.

According to further another aspect of the present invention, there isprovided a resonator including any one of the above-described elasticboundary wave devices.

According to further another aspect of the present invention, there isprovided a filter including any one of the above-described elasticboundary wave devices.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the present invention will be described indetail with reference to the following drawings, wherein:

FIG. 1 shows insertion loss of a conventional elastic boundary wavedevice with respect to frequency;

FIG. 2 is a cross-sectional view of an elastic boundary wave deviceemployed in a first exemplary embodiment of the present invention;

FIG. 3 is a cross-sectional view of a fundamental unit used forsimulation;

FIG. 4 shows k² with respect to the thickness of a silicon oxide film tocompare simulation results and measurement results;

FIG. 5A and FIG. 5B show the insertion loss of S1 and S2 of FIG. 4 withrespect to the frequency;

FIG. 6A and FIG. 6B show the insertion loss of S3 and S4 of FIG. 4 withrespect to the frequency;

FIG. 7A and FIG. 7B show the insertion loss of S5 and S6 of FIG. 4 withrespect to the frequency;

FIG. 8 shows first simulation results;

FIG. 9 shows second simulation results;

FIG. 10 shows third simulation results;

FIG. 11 shows fourth simulation results;

FIG. 12 shows fifth simulation results;

FIG. 13 shows sixth simulation results;

FIG. 14 shows seventh simulation results;

FIG. 15 shows eighth simulation results;

FIG. 16 shows ninth simulation results;

FIG. 17 shows tenth simulation results;

FIG. 18 shows eleventh simulation results;

FIG. 19 shows twelfth simulation results;

FIG. 20 shows thirteenth simulation results;

FIG. 21 shows fourteenth simulation results;

FIG. 22 shows fifteenth simulation results;

FIG. 23 shows sixteenth simulation results;

FIG. 24 shows seventeenth simulation results;

FIG. 25 shows eighteenth simulation results;

FIG. 26 shows nineteenth simulation results;

FIG. 27 shows twentieth simulation results;

FIG. 28 shows twenty-first simulation results;

FIG. 29 shows twenty-second simulation results;

FIG. 30 shows twenty-third simulation results;

FIG. 31 shows twenty-fourth simulation results;

FIG. 32 shows twenty-fifth simulation results;

FIG. 33 shows twenty-sixth simulation results;

FIG. 34 shows twenty-seventh simulation results;

FIG. 35 shows twenty-eighth simulation results;

FIG. 36 shows twenty-ninth simulation results;

FIG. 37 shows thirtieth simulation results;

FIG. 38 shows thirty-first simulation results;

FIG. 39 shows thirty-second simulation results;

FIG. 40 shows thirty-third simulation results;

FIG. 41 shows thirty-fourth simulation results;

FIG. 42 shows thirty-fifth simulation results;

FIG. 43 is a cross-sectional view of an elastic boundary wave deviceemployed in a second exemplary embodiment of the present invention;

FIG. 44 is a cross-sectional view of an elastic boundary wave deviceemployed in a third exemplary embodiment of the present invention;

FIG. 45 is a plan view of a resonator employed in a fourth exemplaryembodiment of the present invention;

FIG. 46 is a plan view of a filter employed in a fifth exemplaryembodiment of the present invention;

FIG. 47 shows thirty-sixth simulation results;

FIG. 48 shows thirty-seventh simulation results;

FIG. 49 shows thirty-eighth simulation results;

FIG. 50 shows thirty-ninth simulation results;

FIG. 51 shows forty simulation results;

FIG. 52 shows forty-first simulation results;

FIG. 53 shows forty-second simulation results;

FIG. 54 shows forty-third simulation results;

FIG. 55 shows forty-fourth simulation results;

FIG. 56 shows forty-fifth simulation results;

FIG. 57 shows forty-sixth simulation results;

FIG. 58 shows forty-seventh simulation results;

FIG. 59 shows forty-eighth simulation results;

FIG. 60 shows forty-ninth simulation results;

FIG. 61 shows fifty simulation results;

FIG. 62 shows fifty-first simulation results;

FIG. 63 shows fifty-second simulation results;

FIG. 64 shows fifty-third simulation results;

FIG. 65 shows fifty-fourth simulation results;

FIG. 66 shows fifty-fifth simulation results; and

FIG. 67 shows fifty-sixth simulation results.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

A description will now be given, with reference to the accompanyingdrawings, of exemplary embodiments of the present invention.

First Exemplary Embodiment

The inventors of the present invention ran a simulation by means of thefinite element method and calculated the magnitude of electromechanicalcoupling coefficient k² of the Stoneley wave in elastic boundary wavedevices having various structures, in order to suppress the Stoneleywave. FIG. 2 is a cross-sectional view of an elastic boundary wavedevice used in the calculation. There are provided an electrode 16having a main component of Cu (Copper) on a rotation Y plate LiNbO₃substrate (LN substrate) 10. The electrode 16 is an interdigitaltransducer (IDT) or a comb-like electrode, and excites the elasticwaves. There is provided on the substrate 10, a silicon oxide (SiO₂)film 12 to cover the electrode 16. There is also provided on the siliconoxide film 12, an oxide aluminum (Al₂O₃) film 14 (medium membrane).

Parameters used in the simulation include: ratio “a” Cu density (8.92g/cm³) in the density of the material used as the electrode 16;wavelength “A” of an elastic wave excited by the electrode 16 (namely,distance between every other electrode fingers); rotation Y cut angle“θ” of the substrate 10; film thickness “h” of the electrode 16;thickness “H” of the silicon oxide film 12. In the simulation, oneelectrode finger shown in FIG. 2 is a fundamental unit, as shown in FIG.3, and the calculation is performed when the fundamental units arerepeated up to infinity. In the calculation results described herein, k²of the elastic boundary wave having a main component of SH wave ranges0.04 to 0.15, and is strong enough to compose a filter of high-frequencyband. Also, judging from FIG. 4 and FIG. 8, k² becomes negative in somecases in FIG. 19; however, the absolute value of the calculated k²should be employed in a normal situation. For this reason, k² inabsolute values are shown in FIG. 20 through FIG. 42, and in FIG. 47through FIG. 67. When k² is represented as 0.00015 or less, the absolutevalues of the calculation result k² denotes 0.00015 or less.

In order to examine whether k² of the actual elastic boundary wavedevice is calculated with accuracy in the simulation, k² of the Stoneleywave of the simulation result is compared with that of the elasticboundary wave device actually produced. The solid line in FIG. 4represents that λ=1.982 μm, h=188 nm, and θ=30°. That is to say, FIG. 4shows the calculation results of the dependency of k² with respect toSiO₂ film thickness (H/λ), where λ=0.095. In addition, other elasticboundary wave devices were respectively produced to have the SiO₂ filmthicknesses (H/λ) of 0.33, 0.38, 0.42, 0.45, 0.52, and 0.58, with theuse of same λ, h, and θ, and the frequency characteristics thereof weremeasured. FIG. 5A through FIG. 7B respectively show the measurementresults of the frequency characteristics of the insertion loss of theelastic boundary wave devices in the one-port resonators produced. S1,S2, S3, S4, S5, and S6 of FIG. 4 respectively represent k² of theStoneley wave in each of the elastic boundary wave devices. FIG. 5Athrough FIG. 7B respectively correspond to the measurement results ofthe elastic boundary wave devices produced under the conditionsrepresented by S1, S2, S3, S4, S5, and S6 shown in FIG. 4. Judging fromFIG. 4, the simulations that the inventors of the present inventioncarried out are very similar to the actual measurement results. In eachof FIG. 5A and FIG. 5B, a large response of the Stoneley wave isrespectively observed. However, the Stoneley wave is smaller in FIG. 6A,and becomes further smaller in FIG. 6B. In FIG. 7A and FIG. 7B, theresponse of the Stoneley wave is no longer observed. When theaforementioned measurement results are compared with the calculationresults shown in FIG. 4, the response of the Stoneley wave is very smalland actually causes no problem in a case where the value of k² of theStoneley wave is equal to or smaller than 0.00015.

Crystal is a material used as a medium of surface acoustic wave devicesand having a small value of k² of a surface acoustic wave, which is afunction of the surface acoustic wave devices. The k² of crystal is0.001. Therefore, at least the surface acoustic wave device thatincludes crystal is demanded to have k² of the Stoneley wave smallerthan that of the surface acoustic wave used as a function thereof. Thatis to say, k² of the Stoneley wave is demanded to be equal to or smallerthan 0.001.

FIG. 8 through FIG. 19 are graphs showing the simulation results of theelectromechanical coupling coefficient k² of the Stoneley wave withrespect to SiO₂ film thickness (H/λ). FIG. 8 through FIG. 19respectively show the results where electrode film thicknesses h arerespectively 0.03λ/a, 0.045λ/a, 0.06λ/a, 0.07λ/a, 0.075λ/a, 0.08λ/a,0.085λ/a, 0.09λ/a, 0.095λ/a, 0.1λ/a, 0.105λ/a, and 0.12λ/a. It isassumed that each calculation point represents a range between middlepoints of both adjacent calculation points. Specifically, for example,in FIG. 10, it is assumed that the calculation result represents0.0525λ/a≦h<0.065λ/a, where h=0.06λ/a, since 0.0525λ/a is a middle pointof h=0.06λ/a and h=0.045λ/a of FIG. 8 and FIG. 9 and 0.065λ/a is amiddle point of h=0.06λ/a and h=0.07λ/a of FIG. 11. On the other hand,if there is no calculation value at one of the adjacent points as shownin FIG. 8, it is assumed that FIG. 8 represents the calculation value ofFIG. 8 and a middle point of those of FIG. 8 and the other adjacentpoint. For example, in FIG. 8, it is assumed that the calculation resultrepresents 0.045λ/a≦h<0.0525λ/a, since the calculation point h=0.045λ/ain FIG. 8 and 0.0525λ/a is a middle point of h=0.045λ/a of FIG. 8 andFIG. 9 and the calculation point h=0.06λ/a of FIG. 10. In a similarmanner, in FIG. 8, it is assumed that the line θ=26° represents a rangeof 25°≦θ<26.5°, where θ=25° is a middle point of θ=26° and θ=24°, andθ=26.5° is a middle point of θ=26° and θ=27°.

Referring to FIG. 8 through FIG. 19, ranges where k² of the Stoneleywave is equal to or smaller than 0.00015 are obtained. It is thereforepossible to cause k² of the Stoneley wave to be equal to or smaller than0.00015, by setting the parameters of the elastic boundary wave deviceto have any one of the ranges shown in FIG. 8 through FIG. 19. In FIG. 8through FIG. 19, solid lines represent the calculation results of rangeswhere k² is equal to or smaller than 0.00015 and dotted lines representthose of remaining ranges.

As shown in FIG. 8 and FIG. 9, there are ranges where k² is equal to orsmaller than 0.00015, when 0.045λ/a≦h<0.0525λ/a, and

when 25°≦θ<26.5°, 0.39λ≦H<0.46λ,

when 26.5°≦θ<27.5°, 0.41λ≦H<0.48λ,

when 27.5°≦θ<28.5°, 0.42λ≦H<0.51λ,

when 28.5°≦θ<29.5°, 0.43λ≦H<0.53λ,

when 29.5°≦θ<30.5°, 0.45λ≦H<0.56λ,

when 30.5°≦θ<31.5°, 0.46λ≦H<0.58λ,

when 31.5°≦θ<32.5 , 0.47λ≦H<0.61λ,

when 32.5°≦θ<33.5°, 0.48λ≦H<0.64λ,

when 33.5°≦θ<35°, 0.48λ≦H<0.67λ,

when 35°≦θ<37.5°, 0.5λ≦H<0.74λ,

when 37.5°≦θ<42°, 0.52λ≦H<0.8λ,

when 42°≦θ<57°, 0.55λ≦H<0.8λ,

when 57°≦θ<63°, 0.51λ≦H<0.8λ,

when 63°≦θ<69°, 0.46λ≦H<0.8λ,

when 69°≦θ<75°, 0.39λ≦H<0.8λ,

when 75°≦θ<99°, 0.3λ≦H<0.8λ, and

when 99°≦θ<105°, 0.58λ≦H<0.8λ.

As shown in FIG. 10, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0525λ/a≦h<0.065λ/a and

when 24°≦θ<25°, 0.3λ≦H<0.32λ,

when 25°≦θ<26.5°, 0.3λ≦H<0.37λ,

when 26.5°≦θ<27.5°, 0.33λ≦H<0.38λ,

when 27.5°≦θ<28.5°, 0.34λ≦H<0.41λ,

when 28.5°≦θ<29.5°, 0.37λ≦H<0.43λ,

when 29.5°≦θ<30.5°, 0.39λ≦H<0.44λ,

when 30.5°≦θ<31.5°, 0.42λ≦H<0.47λ,

when 31.5°≦θ<32.5°, 0.44λ≦H<0.48λ,

when 32.5°≦θ<33.5°, 0.47λ≦H<0.49λ,

when 33.5°≦θ<34.5°, 0.47λ≦H<0.51λ,

when 34.5°≦θ<35.5°, 0.48λ≦H<0.57λ,

when 35.5°≦θ<36.5°, 0.5λ≦H<0.62λ,

when 36.5°≦θ<38°, 0.52λ≦H<0.67λ,

when 38°≦θ<40.5°, 0.54λ≦H<0.79λ,

when 40.5°≦θ<43.5°, 0.58λ≦H<0.8λ,

when 43.5°≦θ<46.5°, 0.61λ≦H<0.8λ,

when 46.5°≦θ<51°, 0.64λ≦H<0.8λ,

when 51°≦θ<57°, 0.69λ≦H<0.8λ, and

when 57 ≦θ<63°, 0.78λ≦H<0.8 λ.

As shown in FIG. 11, there are ranges where k² is equal to or smallerthan 0.00015, when 0.065λ/a≦h<0.0725λ/a and

when 25.5°≦θ<26.5°, 0.3λ≦H<0.32λ,

when 26.5°≦θ<27.5°, 0.3λ≦H<0.36λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.38λ,

when 28.5°≦θ<29.5°, 0.32λ≦H<0.43λ,

when 29.5°≦θ<30.5°, 0.34λ≦H<0.46λ,

when 30.5°≦θ<31.5°, 0.36λ≦H<0.5λ,

when 31.5°≦θ<32.5°, 0.39λ≦H<0.55λ,

when 32.5°≦θ<33.5°, 0.43λ≦H<0.6λ,

when 33.5°≦θ<35°, 0.46λ≦H<0.66λ,

when 35°≦θ<36.5°, 0.54λ≦H<0.8λ,

when 36.5°≦θ<37.5°, 0.59λ≦H<0.8λ,

when 37.5°≦θ<38.5°, 0.65λ≦H<0.8λ, and

when 38.5°≦θ<39°, 0.73λ≦H<0.8 λ.

As shown in FIG. 12, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0725λ/a≦h<0.0775λ/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.35λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.39λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.43λ,

when 29.5°≦θ<30.5°, 0.33λ≦H<0.49λ,

when 30.5°≦θ<31.5°, 0.35λ≦H<0.56λ,

when 31.5°≦θ<32.5°, 0.39λ≦H<0.63λ,

when 32.5°≦θ<33.5°, 0.43λ≦H<0.75λ,

when 33.5°≦θ<34.5°, 0.47λ≦H<0.8λ,

when 34.5°≦θ<35.5°, 0.52λ≦H<0.8λ,

when 35.5°≦θ<36.5°, 0.57λ≦H<0.8λ,

when 36.5°≦θ<37.5°, 0.63λ≦H<0.8λ, and

when 37.5°≦θ<38.5°, 0.72λ≦H<0.8 λ.

As shown in FIG. 13, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0775λ/a≦h<0.0825λ/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.34λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.41λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.47λ,

when 29.5°≦θ<30.5°, 0.32λ≦H<0.56λ,

when 30.5°≦θ<31.5°, 0.36λ≦H<0.69λ,

when 31.5°≦θ<32.5°, 0.39λ≦H<0.8λ,

when 32.5°≦θ<33.5°, 0.44λ≦H<0.8λ,

when 33.5°≦θ<35°, 0.5λ≦H<0.8λ,

when 35°≦θ<36.5°, 0.65λ≦H<0.8λ, and

when 36.5°≦θ<38°, 0.77λ≦H<0.8 λ.

As shown in FIG. 14, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0825λ/a≦h<0.0875λ/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.36λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.44λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.57λ,

when 29.5°≦θ<30.5°, 0.32λ≦H<0.8λ,

when 30.5°≦θ<31.5°, 0.37λ≦H<0.8λ,

when 31.5°≦θ<32.5°, 0.43λ≦H<0.8λ,

when 32.5°≦θ<33.5°, 0.51λ≦H<0.8λ,

when 33.5°≦θ<34.5°, 0.59λ≦H<0.8λ, and

when 34.5°≦θ<35.5°, 0.72λ≦H<0.8 λ.

As shown in FIG. 15, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0875λ/a≦h<0.0925λ/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.39λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.58λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.8λ,

when 29.5°≦θ<30.5°, 0.33λ≦H<0.8λ,

when 30.5°≦θ<31.5°, 0.43λ≦H<0.8λ,

when 31.5°≦θ<32.5°, 0.53λ≦H<0.8λ, and

when 32.5°≦θ<33.5°, 0.67λ≦H<0.8 λ.

As shown in FIG. 16, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0925λ/a≦h<0.0975×/a and

when 26.5°≦θ<27.5°, 0.3λ≦H<0.63λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.8λ,

when 28.5°≦θ<29.5°, 0.3λ≦H<0.8λ,

when 29.5°≦θ<30.5°, 0.42λ≦H<0.8λ, and

when 30.5°≦θ<31.5°, 0.6λ≦H<0.8 λ.

As shown in FIG. 17, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0975λ/a≦h<0.1025λ/a and

when 25.5°≦θ<26.5°, 0.32λ≦H<0.7λ,

when 26.5°≦θ<27.5°, 0.3λ≦H<0.8λ,

when 27.5°≦θ<28.5°, 0.3λ≦H<0.8λ, and

when 28.5°≦θ<29.5°, 0.45λ≦H<0.8λ.

As shown in FIG. 18, there are ranges where k² is equal to or smallerthan 0.00015, when 0.1025λ/a≦h<0.1125λ/a and

when 24.5°≦θ<25.5°, 0.6λ≦H<0.8λ,

when 25.5°≦θ<26.5°, 0.3λ≦H<0.8λ,

when 26.5°≦θ<27.5°, 0.3λ≦H<0.8λ, and

when 27.5°≦θ<28.5°, 0.3λ≦H<0.33 λ or 0.64λ≦H<0.8 λ.

As shown in FIG. 19, there are ranges where k² is equal to or smallerthan 0.00015, when 0.1125λ/a≦h<0.12λ/a and

when 22.5°≦θ<23.5°, 0.47λ≦H<0.76λ, and

when 23.5°≦θ<24.5°, 0.36λ≦H<0.45 λ.

FIG. 20 through FIG. 31 are graphs showing the electromechanicalcoupling coefficient k² of the Stoneley wave with respect to SiO₂ filmthickness (H/λ) and an electrode film pressure (h/λ). FIG. 20 throughFIG. 31 respectively show results when Y-cut angles are 24°, 26°, 27°,28°, 29°, 30°, 31°, 32°, 33°, 34°, 36°, and 39°. As described withreference to FIG. 8 through FIG. 19, it is assumed that each calculationpoint represents a range between middle points with both adjacentcalculation points. There are listed below the graphs shown in FIG. 20through FIG. 31, approximate expressions in the curve of the first orsecond order when k² is equal to 0.00015. From the curves shown, rangeswhere k² is equal to or smaller than 0.00015 are obtained from eachgraph. It is therefore possible to cause k² of the Stoneley wave to beequal to or smaller than 0.00015, by setting the parameters of theelastic boundary wave device to have any one of the ranges shown in FIG.20 through FIG. 31.

As shown in FIG. 20, there are ranges where k² is equal to or smallerthan 0.00015, when 24°≦θ<25°, and

when 0.35≦H/λ<0.45, h/(λ·a)≦0.12,

when 0.45≦H/λ<0.5, h/(λ·a)≦−0.08 H/λ+0.15, and

when 0.5≦H/λ<0.8, h/(λ·a)≦0.116, and additionally,

when 0.35≦H/λ<0.5, h/(λ·a)≧−0.047 H/λ+0.136 and

when 0.5<H/λ≦0.8, h/(λ·a)≧−0.01H/λ+0.118.

Alternatively, when 24°≦θ<25° and

when 0.3≦H/λ≦0.42, h/(λ·a)≦−0.208 H/λ+0.128, and

when 0.3≦H/λ<0.42, h/(λ·a)≧−0.125H/λ+0.0925.

As shown in FIG. 21, there are ranges where k² is equal to or smallerthan 0.00015, when 25°≦θ≦26.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦−0.05H/λ+0.132 and

when 0.4≦H/λ≦0.8, h/(λ·a)≦0.112, and additionally,

when 0.3≦H/λ≦0.8, h/(λ·a)≧0.1.

Alternatively, when 25°≦θ<26.5° and

when 0.3≦H/λ≦0.4, h/(λ·a)≦−0.3 H/λ+0.17, and additionally,

when 0.3≦H/λ≦0.4, h/(λ·a)≧−0.1 H/λ+0.09.

As shown in FIG. 22, there are ranges where k² is equal to or smallerthan 0.00015, when 26.5°≦θ<27.5°, and

when 0.3≦H/λ<0.35, h/(λ·a)≦0.11,

when 0.35≦H/λ<0.4, h/(λ·a)≦−0.04 H/λ+0.124, and

when 0.4≦H/λ<0.8, h/(λ·a)≦0.108, and additionally,

when 0.3≦H/λ<0.35, h/(λ·)≧0.08,

when 0.35≦H/λ<0.4, h/(λ·a)≧0.2H/λ+0.01, and

when 0.4≦H/λ≦0.8, h/(λ·a)≧0.015H/λ+0.084.

Alternatively, when 26.5°≦θ<27.5° and

when 0.3≦H/λ<0.35, h/(λ·a)≦0.08, and

when 0.35≦H/λ≦0.4, h/(λ·a)≦−0.5 H/λ+0.255, and additionally,

when 0.3≦H/λ≦0.4, h/(λ·a)≧−0.09 H/λ+0.091.

Alternatively, when 26.5°≦θ<27.5° and

when 0.38≦H/λ<0.48, h/(λ·a)≦−0.1 H/λ+0.091, and additionally,

when 0.38≦H/λ<0.48, h/(λ·a)≧−0.1H/λ+0.087.

As shown in FIG. 23, there are ranges where k² is equal to or smallerthan 0.00015, when 27.5°≦θ<28.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦−0.03 H/λ+0.116, and

when 0.4≦H/λ≦0.8, h/(λ·a)≦0.005 H/λ+0.102, and additionally,

when 0.3≦H/λ<0.38, h/(λ·a)≧0.07,

when 0.38≦H/λ<0.4, h/(λ·a)≧0.5 H/λ−0.12,

when 0.4≦H/<0.55, h/(λ·a)≧0.067 H/λ+0.053, and

when 0.55≦H/λ≦0.8, h/(λ·a)≧0.008H/λ+0.0856.

Alternatively, when 27.5°≦θ<28.5° and

when 0.3≦H/λ<0.38, h/(λ·a)≦0.07,

when 0.38≦H/λ<0.41, h/(λ·a)<−0.5 H/λ+0.26,

when 0.41≦H/λ<0.5, h/(λ·a)≦−0.111 H/λ+0.101, and additionally,

when 0.3≦H/<0.35, h/(λ·a)≧−0.16 H/λ+0.116,

when 0.35≦H/<0.4, h/(λ·a)≧−0.1 H/λ+0.095,

when 0.4≦H/λ<0.47, h/(λ·a)≧−0.171 H/λ+0.119, and

when 0.47≦H/≦0.5, h/(λ·a)≧0.233 H/λ−0.0717.

As shown in FIG. 24, there are ranges where k² is equal to or smallerthan 0.00015, when 28.5°≦θ<29.5° and

when 0.3≦H/λ≦0.8, h/(λ·a)≦0.008H/λ+0.0956, and additionally,

when 0.3≦H/λ<0.4, h/(λ·a)≧−0.14 H/λ+0.114,

when 0.4≦H/λ≦0.42, h/(λ·a)≧0.058, and

when 0.42≦H/λ≦0.8, h/(λ·a)≧−0.342 (H/λ)²+0.465H/λ−0.0648.

Alternatively, when 28.5°≦θ<29.5°,

when 0.42≦H/λ<0.45, h/(λ·a)≦0.0052,

when 0.45≦H/λ<0.53, h/(λ·a)≦−0.0875 H/λ+0.0914, and

when 0.53≦H/λ≦0.55, h/(λ·a)≦−0.75 H/λ+0.443, and additionally,

when 0.42≦H/λ<0.46, h/(λ·a)≧−0.175 H/λ+0.121,

when 0.46≦H/λ<0.5, h/(λ·a)≧0.04, and

when 0.5≦H/λ≦0.55, h/(λ·a)≧−0.2 H/λ+0.14.

Alternatively, when 28.5°≦θ<29.5° and

when 0.55≦H/λ<0.58, h/(λ·a)≦0.167H/λ−0.0617, and

when 0.58≦H/λ≦0.75, h/(λ·a)≦−0.0294 H/λ+0.0521, and additionally,

when 0.55≦H/λ≦0.75, h/(λ·a)≧0.03.

As shown in FIG. 25, there are ranges where k² is equal to or smallerthan 0.00015, when 29.5°≦θ<30.5° and

when 0.32≦H/λ≦0.8, h/(λ·a)≦−0.286 (H/λ)²+0.356H/λ−0.0027, andadditionally,

when 0.32≦H/λ<0.4, h/(λ·a)≧3.33 (H/λ)²−2.7 H/λ+0.605,

when 0.4≦H/λ<0.44, h/(λ·a)≧0.058, and

when 0.44≦H/λ≦0.8, h/(λ·a)≧−0.75 (H/λ)²+1.005 H/λ−0.239.

Alternatively, when 29.5°≦θ<30.5°,

when 0.43≦H/λ<0.46, h/(λ·a)≦0.052,

when 0.46≦H/λ<0.57, h/(λ·a)≦−0.0727 H/λ+0.0855,

when 0.57≦H/λ<0.6, h/(λ·a)≦−0.333 H/λ+0.234, and

when 0.6≦H/λ≦0.75, h/(λ·a)≦−0.0267 H/λ+0.05, and additionally,

when 0.43≦H/λ<0.45, h/(λ·a)≧−0.4 H/λ+0.224,

when 0.45≦H/λ<0.55, h/(λ·a)≧−0.14 H/λ+0.107, and

when 0.55≦H/λ≦0.75, h/(λ·a)≧0.03.

As shown in FIG. 26, there are ranges where k² is equal to or smallerthan 0.00015, when 30.5°≦θ<31.5° and

when 0.36≦H/λ≦0.8, h/(λ·a)≦−0.131 (H/λ)²+0.188 H/λ+0.00293, andadditionally,

when 0.36≦H/λ<0.43, h/(λ·a)≧4.64 (H/λ)²−3.95 H/λ+0.902,

when 0.43≦H/λ<0.465, h/(λ·a)≧0.06, and

when 0.465≦H/λ≦0.8, h/(λ·a)≧−0.283 (H/λ)²+0.424H/λ−0.0758.

when 30.5°≦θ<31.5° and

when 0.43≦H/λ<0.465, h/(λ·a)≦0.06,

when 0.465≦H/λ<0.65, h/(λ·a)≦−0.108 H/λ+0.105, and

when 0.65≦H/λ≦0.8, h/(λ·a)≦−0.0333 H/λ+0.0567, and additionally,

when 0.43≦H/λ<0.45, h/(λ·a)≧−0.65 H/λ+0.34,

when 0.45≦H/λ<0.57, h/(λ·a)≧−0.142 H/λ+0.111, and

when 0.57≦H/λ≦0.8, h/(λ·a)≧0.03.

As shown in FIG. 27, there are ranges where k² is equal to or smallerthan 0.00015, when 31.5°≦θ<32.5° and

when 0.39≦H/λ≦0.8, h/(λ·a)≦−0.153 (H/λ)²+0.219 H/λ+0.0169, andadditionally,

when 0.39≦H/λ<0.45, h/(λ·a)≧−0.2 H/λ+0.15,

when 0.45≦H/λ<0.48, h/(λ·a)≧0.6, and

when 0.48≦H/λ≦0.8, h/(λ·a)≧−0.346 (H/λ)²+0.5 H/λ−0.1.

Alternatively, when 31.5°≦θ<32.5° and

when 0.45≦H/λ<0.48, h/(λ·a)≦0.06,

when 0.48≦H/λ<0.65, h/(λ·a)≦−0.135 H/λ+0.125, and

when 0.65≦H/λ≦0.8, h/(λ·a)≦−0.0333 H/λ+0.0587, and additionally,

when 0.45≦H/λ<0.58, h/(λ·a)≧−0.154 H/λ+0.119, and

when 0.58≦H/λ≦0.8, h/(λ·a)≧0.03.

As shown in FIG. 28, there are ranges where k² is equal to or smallerthan 0.00015, when 32.5°≦θ<33.5° and

when 0.43≦H/λ≦0.8, h/(λ·a)≦−1.266 (H/λ)²+1.614 H/λ−0.39, andadditionally,

when 0.43≦H/λ<0.45, h/(λ·)≧−0.4 H/λ+0.242,

when 0.45≦H/λ<0.5, h/(λ·a)≧0.062, and

when 0.5≦H/λ≦0.8, h/(λ·a)≧−0.167 (H/λ)²+0.263 H/λ−0.028.

Alternatively, when 32.5°≦θ<33.5° and

when 0.45≦H/λ<0.5, h/(λ·a)≦0.06 H/λ+0.028,

when 0.5≦H/λ<0.7, h/(λ·a)≦−0.11 H/λ+0.113, and

when 0.7≦H/λ≦0.8, h/(λ·a)≦−0.03 H/λ+0.057, and additionally,

when 0.45≦H/λ<0.48, h/(λ·a)≧−0.3 H/λ+0.19,

when 0.48≦H/λ<0.59, h/(λ·a)≧−0.145 H/λ+0.116, and

when 0.59≦H/λ≦0.8, h/(λ·a)≧0.03.

As shown in FIG. 29, there are ranges where k² is equal to or smallerthan 0.00015, when 33.5°≦θ<35° and

when 0.425≦H/λ≦0.8, h/(λ·a)≦−0.284 (H/λ)²+0.396H/λ−0.0471, andadditionally,

when 0.425≦H/≦0.48, h/(λ·a)≧−0.109 H/λ+0.116,

when 0.48≦H/≦0.57, h/(λ·a)≧0.064, and

when 0.57≦H/≦0.8, h/(λ·a)≧−0.6594 (H/λ)²+0.9382H/λ−0.257.

Alternatively, when 33.5°<θ<35° and

when 0.48≦H/λ≦0.52, h/(λ·a)≦0.064, and

when 0.52≦H/λ≦0.8, h/(λ·a)≦−0.0929 H/λ+0.108, and additionally,

when 0.48≦H/λ≦0.59, h/(λ·a)≧−0.155 H/λ+0.121, and

when 0.59≦H/λ≦0.8, h/(λ·a)≧0.03.

As shown in FIG. 30, there are ranges where k² is equal to or smallerthan 0.00015, when 35°≦θ<37.5° and

when 0.54≦H/λ≦0.8, h/(λ·a)≦−0.273 (H/λ)²+0.415 H/λ−0.0748, andadditionally,

when 0.54≦H/λ<0.62, h/(λ·a)≧0.06, and

when 0.62≦H/λ≦0.8, h/(λ·a)≧−0.5(H/λ)²+0.76 H/λ−0.219.

Alternatively, when 35°≦θ<37.5° and

when 0.5≦H/λ<0.62, h/(λ·a)≦0.06, and

when 0.62≦H/λ≦0.8, h/(λ·a)≦−0.117 H/λ+0.132, and additionally,

when 0.5≦H/λ<0.6, h/(λ·a)≧−0.16 H/λ+0.126, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧0.03.

As shown in FIG. 31, there are ranges where k² is equal to or smallerthan 0.00015, when 37.5°<θ<39° and

when 0.52≦H/λ<0.6, h/(λ·a)≦0.2 H/λ−0.054,

when 0.6≦H/λ<0.7, h/(λ·a)≦0.066,

when 0.7≦H/λ≦0.8, h/(λ·a)≦0.09 H/λ+0.003, and additionally,

when 0.52≦H/λ<0.62, h/(λ·a)≧−0.2 H/λ+0.154, and

when 0.62≦H/λ<0.8, h/(λ·a)≧0.03.

FIG. 32 through FIG. 42 are graphs showing the electromechanicalcoupling coefficient k² of the Stoneley wave with respect to SiO₂ filmthickness (H/λ) and Y-cut angle θ. FIG. 32 through FIG. 42 respectivelyshow the results where electrode film thicknesses h are respectively0.03λ/a, 0.045λ/a, 0.06λ/a, 0.07λ/a, 0.075λ/a, 0.08λ/a, 0.085λ/a,0.09λ/a, 0.095λ/a, 0.10λ/a, and 0.105λ/a. As described in FIG. 8 throughFIG. 19, it is assumed that each calculation point represents a rangebetween middle points with both adjacent calculation points. There arelisted below the graphs shown in FIG. 32 through FIG. 42, approximateexpressions in the curve of the first or second order when k² is equalto 0.00015. From the curves shown in each graph, ranges where k² isequal to or smaller than 0.00015 are obtained. It is therefore possibleto cause k² of the Stoneley wave to be equal to or smaller than 0.00015,by setting the parameters of the elastic boundary wave device to haveany one of the ranges shown in FIG. 32 through FIG. 42.

As shown in FIG. 32, there are ranges where k² is equal to or smallerthan 0.00015, when 0.03λ/a≦h<0.0375λ/a and

when 0.3≦H/λ≦0.8, θ≦75 (H/λ)²−82.5 H/λ+103.687, and additionally,

when 0.3≦H/λ<0.65, θ≧−85.7 H/λ+97.7, and

when 0.65≦H/λ≦0.8, θ≧42.

Alternatively,

when 0.03λ/a≦h<0.0375λ/a and

when 0.45≦H/λ<0.65, θ≦120H/λ−36, and

when 0.65≦H/λ≦0.8, θ≦42, and additionally,

when 0.45≦H/λ<0.5, θ≧18, and

when 0.5≦H/λ≦0.8, θ≧40H/λ−2.

As shown in FIG. 33, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0375λ/a≦h<0.0525λ/a and

when 0.3≦H/λ≦0.8, θ≦24 H/λ+88.8, and additionally,

when 0.3≦H/λ<0.55, θ≧−120 H/λ+114, and

when 0.55≦H/λ≦0.8, θ≧48.

Alternatively,

when 0.0375λ/a≦h<0.0525λ/a and

when 0.43≦H/λ<0.55, θ≦180 H/λ−51, and

when 0.55≦H/≦0.8, θ≦48, and additionally,

when 0.43≦H/λ≦0.8, θ≧34.3 H/λ+11.6.

As shown in FIG. 34, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0525λ/a≦h<0.065λ/a and

when 0.45≦H/λ≦0.8, θ≦80 H/λ−4, and additionally,

when 0.45≦H/λ≦0.8, θ≧20H/λ+23.

As shown in FIG. 35, there are ranges where k² is equal to or smallerthan 0.00015, when 0.065λ/a≦h<0.0725λ/a and

when 0.3≦H/λ<0.7, θ<−26.7 (H/λ)²+52 H/λ+15.5, and

when 0.7≦H/λ≦0.8, θ≦25 H/λ+21, and additionally,

when 0.3≦H/λ≦0.8, θ≧−16.7 (H/λ)²+38.3 H/λ+16.

As shown in FIG. 36, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0725×/a≦h<0.0775λ/a and

when 0.3≦H/λ≦0.8, θ<−25 (H/λ)²+47.5 H/λ+17, and additionally,

when 0.3≦H/λ≦0.8, θ≧−25 (H/λ)²+42.5 H/λ+15.2.

As shown in FIG. 37, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0775×/a≦h<0.0825λ/a and

when 0.3≦H/λ≦0.8, θ≦−21.4 (H/λ)²+38.2 H/λ+20.1, and additionally,

when 0.3≦H/λ≦0.8, θ≧−23.3 (H/λ)²+35.8H/λ+17.4.

As shown in FIG. 38, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0825λ/a≦h<0.0875λ/a and

when 0.3≦H/λ≦0.8, θ≦−13.3(H/λ)²+24.7H/λ+24, and additionally,

when 0.3≦H/λ≦0.8, θ≧−16 (H/λ)²+25.6 H/λ+19.8.

As shown in FIG. 39, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0875λ/a≦h<0.0925λ/a, and

when 0.3≦H/λ<0.55, θ≦10 H/λ+26.5, and

when 0.55≦H/λ≦0.8, θ≦6 H/λ+28.7, and additionally,

when 0.3≦H/λ≦0.8, θ≧4 H/λ+25.3.

As shown in FIG. 40, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0925λ/a≦h<0.0975λ/a and

when 0.3≦H/λ≦0.8, θ≦4 H/λ+28.3, and additionally,

when 0.3≦H/λ≦0.8, θ≧2 H/λ+25.9.

As shown in FIG. 41, there are ranges where k² is equal to or smallerthan 0.00015, when 0.0975λ/a≦h<0.1025λ/a and

when 0.3≦H/λ≦0.8, θ≦2 H/λ+28.2, and additionally,

when 0.3≦H/λ≦0.8, θ≧26.

As shown in FIG. 42, there are ranges where k² is equal to or smallerthan 0.00015, when 0.1025λ/a≦h<0.105λ/a and

when 0.3≦H/λ≦0.8, θ≦28, and additionally,

when 0.3≦H/λ<0.5, θ≧−5 H/λ+27.5, and

when 0.5≦H/λ≦0.8, θ≧25.

As stated heretofore, it is possible to make the k² of the Stoneley waveequal to or smaller than 0.00015, by setting the parameters of theelastic boundary wave device to have any of the ranges shown in FIG. 8through FIG. 42, thereby reducing the influence on the elastic boundarywave device.

In accordance with the first exemplary embodiment of the presentinvention, the propagation direction of the boundary wave having a maincomponent of SH is an x-axis direction of LN substrate.

In the first exemplary embodiment of the present invention, adescription has been given of the oxide aluminum film 14 serving as amedium membrane on the silicon oxide film 12; however, in a case wherethe sound velocity of the medium membrane is faster than that of SiO₂and the film thickness of the medium membrane is as thick as 1λ or more,the above-described simulation may be employed. When the sound velocityof the medium membrane is faster than that of the silicon oxide film 12,the elastic boundary wave is confined in the silicon oxide film 12. As amedium membrane having a sound velocity faster than that of the siliconoxide film 12, the medium membrane preferably includes any one ofsilicon nitride, aluminum silicon, aluminum oxide, and silicon.

Preferably, the density of the electrode 16 is greater than that of thesilicon oxide film 12. This allows the increase of the reflection of theelastic boundary wave. Furthermore, as the electrode 16, copper (Cu) ispreferably included. Since copper has a higher density and lowerresistance than the silicon oxide film 12, the electrical loss can belowered. Also, the silicon oxide film 12 may be made of a film thatmainly includes silicon oxide within a range where the above-describedsimulation can be employed.

Second Exemplary Embodiment

The simulation results obtained in the first exemplary embodiment of thepresent invention may be employed for a case where the electrode 16 hasa multilayer structure with two or more layers. Referring to FIG. 43,the electrode 16 is composed of a titanium (Ti) layer 16 a and a cupper(Cu) layer 16 b, as compared with the electrode 16 in FIG. 2.Hereinafter, in the second exemplary embodiment of the presentinvention, the same components and configurations as those employed inFIG. 2 have the same reference numerals and a detailed explanation willbe omitted. As shown in FIG. 43, the electrode 16 may have a multilayerstructure where the Ti layer 16 a is provided on the substrate 10 andthe Cu layer 16 b is provided on the Ti layer 16 a. This can promote theadherence between the electrode 16 and the substrate 10. In the secondexemplary embodiment of the present invention, an average density “r” ofthe electrode 16 is expressed as:r=p×b/(b+c)+q×c/(b+c),

where “p” is the density of the Cu layer 16 b, “q” is the density of theTi layer 16 a, “b” is the film thickness of the Cu layer 16 b, and “c”is the film thickness of the Ti layer 16 a.

Also, the simulation results described in the first exemplary embodimentof the present invention may be used by setting:a=r/density of Cu (8.92 g/cm³).

The simulation results described in the first exemplary embodiment ofthe present invention may be employed by calculating the average densityof the electrode 16 with the same calculation method and then obtaining“a”, also in a case where the electrode 16 has three or more layers.Herein, the Cu layer 16 b includes cupper such that the reflection ofthe elastic boundary wave can be increased and the loss thereof can bedecreased with a low resistance. The Ti layer 16 a includes titaniumsuch that the electrode 16 and the substrate 10 can be adhered to eachother.

Third Exemplary Embodiment

The simulation results described in the first exemplary embodiment ofthe present invention may be used for a case where there is provided abarrier layer 18 that covers the electrode 16. Referring to FIG. 44,there is provided the barrier layer 18 made of a silicon nitride (Si₃N₄)film and covering the electrode 16. Hereinafter, in the third exemplaryembodiment of the present invention, the same components andconfigurations as those employed in FIG. 2 have the same referencenumerals and a detailed explanation will be omitted. The barrier layer18 prevents the metal included in the electrode 16 from dissipating intothe silicon oxide film 12. In particular, when the electrode 16 includescopper, copper easily dissipates into the silicon oxide film 12. Hence,it is preferable that barrier layer 18 be provided. It is alsopreferable that a silicon nitride film be employed as the barrier layer18 because of the barrier capability and the ease of formation thereof.In addition to the silicon nitride film, a film having the capabilitythat suppresses the dissipation of the metal included in the electrode16 into the silicon oxide film may be employed.

Fourth Exemplary Embodiment

A fourth exemplary embodiment of the present invention is an example ofa resonator having any of the elastic boundary wave devices employed inthe first through third exemplary embodiments of the present invention.FIG. 45 is a plan view showing electrodes included in a resonator. Thereare arranged reflectors 26 and 28 at both sides of an elastic boundarywave device 20 having comb-like electrodes. The 20 includes an inputelectrode 22 and an output electrode 24. The reflector 26 and 28 arefabricated simultaneously with the elastic boundary wave device 20 thatincludes the comb-like electrodes. Boundary waves propagating to theboth sides from the elastic boundary wave device 20 are reflected by thereflector 26 and 28. Such reflected boundary waves become standing wavesof the boundary waves in the elastic boundary wave device 20. Theresonator operates in this manner. In accordance with the fourthexemplary embodiment of the present invention, the resonator suppressingthe Stoneley wave is available by configuring the resonator with any ofthe elastic boundary wave devices employed in the first through thirdexemplary embodiments of the present invention. This improves frequencycharacteristics of the resonator.

Fifth Exemplary Embodiment

A fifth exemplary embodiment of the present invention is an example of afour-stage ladder type filter that includes the resonator employed inthe fourth exemplary embodiment of the present invention. FIG. 46 is aplan view showing electrodes included in the ladder type filter employedin the fourth exemplary embodiment of the present invention. There areprovided resonators 32, 34, 36, and 38 connected in series to serve as aseries-arm resonator 30, the resonators being employed in the fourthexemplary embodiment of the present invention. One end of the resonator32 is connected to an input pad electrode 50, and one end of theresonator 38 is connected to an electrode 52. An electrode, not shown,connected by the resonator 32 and the resonator 34 is further connectedto the resonator 40, and an electrode, not shown, connected by theresonator 38 and the resonator 36 is further connected to the resonator42. One end of the resonator 40 is connected to a ground pad electrode54, the one end being not connected by a resonator. One end of theresonator 42 is connected to a ground pad electrode 56, the one endbeing not connected by a resonator. The resonators 40 and 42 function asa parallel-arm resonator. The above-described configuration allows thefilter employed in the fifth exemplary embodiment of the presentinvention to operate as a ladder-type filter. In accordance with thefifth exemplary embodiment, the filter suppressing the Stoneley wave isavailable by configuring the ladder-type filter with any of the elasticboundary wave devices employed in the first through third exemplaryembodiments of the present invention. This improves frequencycharacteristics of the filter. In the fifth exemplary embodiment of thepresent invention, a description has been given of the ladder-typefilter; however, in addition to the ladder-type filter, for example, adouble-mode filter may be configured with any of the elastic boundarywave devices employed in the first through third exemplary embodimentsof the present invention.

FIG. 47 through FIG. 67 are graphs showing the electromechanicalcoupling coefficient k of the Stoneley wave with respect to SiO₂ filmthickness (H/λ) and the electrode film pressure (h/λ), in addition tothe graphs shown in FIG. 20 through FIG. 31 used in the first exemplaryembodiment of the present invention. FIG. 47 through FIG. 67respectively show results of Y-cut angles θ of 0°, 1°, 3°, 6°, 9°, 10°,11°, 12°, 13°, 14°, 15°, 16°, 170°, 18°, 19°, 20°, 21°, 22°, 23°, 24°,and 177°. It is assumed that each calculation point represents a rangebetween middle points with both adjacent calculation points, in asimilar manner as shown in FIG. 20 through FIG. 31. There are listedbelow the graphs shown in FIG. 47 through FIG. 67, approximateexpressions in the curve of the first or second order when k² is equalto 0.00015. It is therefore possible to cause k² of the Stoneley wave tobe equal to or smaller than 0.00015, by setting the parameters of theelastic boundary wave device to have any one of the ranges shown in FIG.47 through FIG. 67.

As shown in FIG. 47, there are ranges where k² is equal to or smallerthan 0.00015, when 0°<θ<0.5° and when 0.6≦H/λ≦0.8, h/(λ·a)≦H/λ. Here,the reason h/(λ·a)≦H/λ is h/(λ·a)>H/λ is not taken into consideration inthe model used for the simulation. Also, when 0.6≦H/λ<0.625, h/(λ·a)≧−2H/λ+1.8, and when 0.625≦H/λ≦0.8, h/(λ·a)≧1.543 (H/λ)²−2.484 H/λ+1.5.

As shown in FIG. 48, there are ranges where k² is equal to or smallerthan 0.00015, when 0.5°<θ<2° and

when 0.508≦H/λ≦0.8, h/(λ·a)≦H/λ, and additionally,

when 0.508≦H/λ<0.531, h/(λ·a)≧−0.3478H/λ+0.6847,

when 0.531≦H/λ<0.6, h/(λ·a)≧−0.6087 H/λ+0.8232, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧0.6 (H/λ)²−0.98 H/λ+0.83.

As shown in FIG. 49, there are ranges where k² is equal to or smallerthan 0.00015, when 2°≦θ<4.5° and

when 0.45≦H/λ≦0.8, h/(λ·a)≦H/λ, and additionally,

when 0.45≦H/λ<0.5, h/(λ·a)≧28.998 (H/λ)²−29.088 H/λ+7.668,

when 0.5≦H/λ<0.65, h/(λ·a)≧1.6 (H/λ)²−2.06H/λ+1.003, and

when 0.65≦H/λ≦0.8, h/(λ·a)≧−0.0733H/λ+0.3877.

As shown in FIG. 50, there are ranges where k² is equal to or smallerthan 0.00015, when 4.5°≦θ<7.5° and

when 0.3625≦H/λ<0.496, h/(λ·a)≦H/λ,

when 0.496≦H/λ<0.55, h/(λ·a)≦−0.111 H/λ+0.5511,

when 0.55≦H/λ<0.65, h/(λ·a)≦3.4 (H/λ)²−4.45 H/λ+1.909,

when 0.65≦H/λ<0.7, h/(λ·a)≦−0.06 H/λ+0.492, and

when 0.7≦H/λ≦0.8, h/(λ·a)≦0.45, and additionally,

when 0.3625≦H/λ<0.3875, h/(λ·a)≧−0.46 H/λ+0.5293,

when 0.3875≦H/λ<0.4, h/(λ·a)≧−2.96 H/λ+1.498,

when 0.4≦H/λ<0.45, h/(λ·a)≧−0.58 H/λ+0.546,

when 0.45≦H/λ<0.6, h/(λ·a)≧1.2667 (H/λ)²−1.503 H/λ+0.705, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧−0.04 H/λ+0.283.

As shown in FIG. 51, there are ranges where k² is equal to or smallerthan 0.00015, when 7.5°≦θ<9.5° and

when 0.315≦H/λ<0.406, h/(λ·a)≦H/λ,

when 0.406≦H/λ<0.419, h/(λ·a)≦−1.077 H/λ+0.8432,

when 0.419≦H/λ<0.45, h/(λ·a)≦61.7512 (H/λ)²−55.565 H/λ+12.8326,

when 0.45≦H/λ<0.6, h/(λ·a)≦1.8667 (H/λ)²−2.233 H/λ+0.96, and

when 0.6≦H/λ≦0.8, h/(λ·a)≦0.2 (H/λ)²−0.32 H/λ+0.412, and additionally,

when 0.315≦H/λ<0.342, h/(λ·a)≧−0.5556 H/λ+0.49,

when 0.342≦H/λ<0.35, h/(λ·a)≧−3.75 H/λ+1.5825,

when 0.35≦H/λ<0.4, h/(λ·a)≧−0.6 H/λ+0.48,

when 0.4≦H/λ<0.55, h/(λ·a)≧1.133 (H/λ)²−1.243 H/λ+0.556, and

when 0.55≦H/λ≦0.8, h/(λ·a)≧0.1067 (H/λ)²−0.18 H/λ+0.2817.

As shown in FIG. 52, there are ranges where k² is equal to or smallerthan 0.00015, when 9.5°≦θ<10.5° and

when 0.31≦H/λ<0.37, h/(λ·a)≦H/λ,

when 0.37≦H/λ<0.383, h/(λ·a)≦0.37,

when 0.383≦H/λ<0.392, h/(λ·a)≦−1.111 H/λ+0.7956,

when 0.392≦H/λ<0.4, h/(λ·a)≦−2.5 H/λ+1.34,

when 0.4≦H/λ<0.45, h/(λ·a)≦12 (H/λ)²−11.1 H/λ+2.86,

when 0.45≦H/λ<0.5, h/(λ·a)≦3.2 (H/λ)²−3.36 H/λ+1.159,

when 0.5≦H/λ<0.61, h/(λ·a)≦0.5455 (H/λ)²−0.7327 H/λ+0.509, and

when 0.61≦H/λ≦0.8, h/(λ·a)≦0.08848 (H/λ)²−0.1616 H/λ+0.3307, andadditionally,

when 0.31≦H/λ<0.331, h/(λ·a)≧−0.4762 H/λ+0.4576,

when 0.331≦H/λ<0.35, h/(λ·a)≧−2.632 H/λ+1.171,

when 0.35≦H/λ<0.4, h/(λ·a)≧−0.5 H/λ+0.425,

when 0.4≦H/λ<0.5, h/(λ·a)≧(H/λ)²−1.09H/λ+0.501, and

when 0.5≦H/λ≦0.8, h/(λ·a)≧0.1 (H/λ)²−0.17 H/λ+0.266.

As shown in FIG. 53, there are ranges where k² is equal to or smallerthan 0.00015, when 10.5°≦θ<11.5° and

when 0.304≦H/λ<0.36, h/(λ·a)≦H/λ,

when 0.36≦H/λ<0.3625, h/(λ·a)≦−4 H/λ+1.8,

when 0.3625≦H/λ<0.375, h/(λ·a)≦−0.8 H/λ+0.64,

when 0.375≦H/λ<0.4, h/(λ·a)≦80.702 (H/λ)²−64.344 H/λ+13.120,

when 0.4≦H/λ<0.5, h/(λ·a)≦3 (H/λ)²−3.091 H/λ+1.051,

when 0.5≦H/λ<0.7, h/(λ·a)≦0.4 (H/λ)²−0.56 H/λ+0.436, and

when 0.7≦H/λ≦0.8, h/(λ·a)≦−0.02 H/λ+0.254, and additionally,

when 0.304≦H/λ<0.329, h/(λ·a)≧−0.56 H/λ+0.474,

when 0.329≦H/λ<0.331, h/(λ·a)≧−15 H/λ+5.225,

when 0.331≦H/λ<0.35, h/(λ·a)≧−1.579 H/λ+0.7826,

when 0.35≦H/λ<0.4, h/(λ·a)≧−0.4 H/λ+0.37,

when 0.4≦H/λ<0.575, h/(λ·a)≧0.4762 (H/λ)²−0.5786 H/λ+0.3652, and

when 0.575≦H/λ≦0.8, h/(λ·a)≧0.0381 (H/λ)²−0.07905 H/λ+0.2229.

As shown in FIG. 54, there are ranges where k² is equal to or smallerthan 0.00015, when 11.5°≦θ<12.5°, and

when 0.3≦H/λ<0.35, h/(λ·a)≦H/λ,

when 0.35≦H/λ<0.358, h/(λ·a)≦−1.25 H/λ+0.7875,

when 0.358≦H/λ<0.3625, h/(λ·a)≦−6.667 H/λ+2.7267,

when 0.3625≦H/λ<0.4, h/(λ·a)≦27.781 (H/λ)²−22.3379 H/λ+4.7569,

when 0.4≦H/λ<0.5, h/(λ·a)≦2.18 (H/λ)²−2.271 H/λ+0.8263,

when 0.5≦H/λ<0.65, h/(λ·a)≦0.44 (H/λ)²−0.578 H/λ+0.4148, and

when 0.65≦H/λ≦0.8, h/(λ·a)≦−0.02667 H/λ+0.2423, and additionally,

when 0.3≦H/λ<0.308, h/(λ·a)≧−0.5 H/λ+0.45,

when 0.308≦H/λ<0.35, h/(λ·a)≧25.1541 (H/λ)²−18.099 H/λ+3.4683,

when 0.35≦H/λ<0.45, h/(λ·a)≧1.8 (H/λ)²−1.69 H/λ+0.586,

when 0.45≦H/λ<0.6, h/(λ·a)≧0.3333 (H/λ)²−0.4167 H/λ+0.31, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧−0.02 H/λ+0.192.

As shown in FIG. 55, there are ranges where k² is equal to or smallerthan 0.00015, when 12.5°≦θ<13.5° and

when 0.3≦H/λ<0.32, h/(λ·a)≦H/λ,

when 0.32≦H/λ<0.35, h/(λ·a)≦−H/λ+0.64,

when 0.35≦H/λ<0.373, h/(λ·a)≦−1.3044 H/λ+0.7465,

when 0.373≦H/λ<0.4, h/(λ·a)≦−0.6296 H/λ+0.4949,

when 0.4≦H/λ<0.5, h/(λ·a)≦1.6 (H/λ)²−1.66 H/λ+0.651,

when 0.5≦H/λ<0.65, h/(λ·a)≦0.4667 (H/λ)²−0.61 H/λ+0.4093, and

when 0.65≦H/λ≦0.8, h/(λ·a)≦−0.02 H/λ+0.223, and additionally,

when 0.3≦H/λ<0.35, h/(λ·a)≧−0.8 H/λ+0.48,

when 0.35≦H/λ<0.45, h/(λ·a)≧−0.2 H/λ+0.27,

when 0.45≦H/λ<0.625, h/(λ·a)≧0.09524 (H/λ)²−0.1595 H/λ+0.2325, and

when 0.65≦H/λ≦0.8, h/(λ·a)≧−0.01143 H/λ+0.1771.

As shown in FIG. 56, there are ranges where k² is equal to or smallerthan 0.00015, when 13.5°≦θ≦14.5° and

when 0.3≦H/λ<0.318, h/(λ·a)≦H/λ,

when 0.318≦H/λ<0.325, h/(λ·a)≦−4 H/λ+1.59,

when 0.325≦H/λ<0.4, h/(λ·a)≦6.933 (H/λ)²−5.88 H/λ+1.4687,

when 0.4≦H/λ<0.585, h/(λ·a)≦0.6618 (H/λ)²−0.7924 H/λ+0.437, and

when 0.585≦H/λ≦0.8, h/(λ·a)≦0.11527 (H/λ)²−0.1829 H/λ+0.2676, andadditionally,

when 0.3≦H/λ<0.35, h/(λ·a)≧−0.6 H/λ+0.4,

when 0.35≦H/λ<0.475, h/(λ·a)≧0.8 (H/λ)²−0.82 H/λ+0.379,

when 0.475≦H/λ<0.65, h/(λ·a)≧0.2095 (H/λ)²−0.2814 H/λ+0.2564, and

when 0.65≦H/λ≦0.8, h/(λ·a)²−0.0133 H/λ+0.1707.

As shown in FIG. 57, there are ranges where k² is equal to or smallerthan 0.00015, when 14.5°≦θ<15.5° and

when 0.3≦H/λ<0.304, h/(λ·a)≦H/λ,

when 0.304≦H/λ<0.308, h/(λ·a)≦−1.25H/λ+0.685,

when 0.308≦H/λ<0.321, h/(λ·a)≦−2.308 H/λ+1.011,

when 0.321≦H/λ<0.375, h/(λ·a)≦11.239 (H/λ)²−8.748 H/λ+1.920,

when 0.375≦H/λ<0.5, h/(λ·a)≦1.1733 (H/λ)²−1.2347 H/λ+0.518,

when 0.5≦H/λ<0.65, h/(λ·a)≦0.267 (H/λ)²−0.36 H/λ+0.3073, and

when 0.65≦H/λ≦0.8, h/(λ·a)≦−0.01333 H/λ+0.1947, and additionally,

when 0.3≦H/λ<0.35, h/(λ·a)≧−0.5 H/λ+0.355,

when 0.35≦H/λ<0.4, h/(λ·a)≧−0.2 H/λ+0.25,

when 0.4≦H/λ<0.5, h/(λ·a)≧−0.1 H/λ+0.21,

when 0.5≦H/λ<0.7, h/(λ·a)≧−0.03 H/λ+0.175, and

when 0.7≦H/λ≦0.8, h/(λ·a)≧0.154.

As shown in FIG. 58, there are ranges where k² is equal to or smallerthan 0.00015, when 15.5°≦θ<16.5° and

when 0.3≦H/λ<0.308, h/(λ·a)≦−1.25 H/λ+0.675,

when 0.308≦H/λ<0.311, h/(λ·a)≦−10 H/λ+3.37,

when 0.311≦H/λ<0.321, h/(λ·a)≦−2 H/λ+0.882,

when 0.321≦H/λ<0.4, h/(λ·a)≦5.9188 (H/λ)²−4.799 H/λ+1.171,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.711 (H/λ)²−0.7956 H/λ+0.4024,

when 0.55≦H/λ≦0.8, h/(λ·a)≦0.128 (H/λ)²−0.197 H/λ+0.2495, andadditionally,

when 0.3≦H/λ<0.35, h/(λ·a)≧−0.4 H/λ+0.31,

when 0.35≦H/λ<0.5, h/(λ·a)≧0.3556 (H/λ)²−0.4089 H/λ+0.2696, and

when 0.5≦H/λ≦0.8, h/(λ·a)≧0.08762 (H/λ)²−0.1306 H/λ+0.1974.

As shown in FIG. 59, there are ranges where k² is equal to or smallerthan 0.00015, when 16.5°≦θ<17.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦8.6 (H/λ)²−6.75 H/λ+1.511,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.467 (H/λ)²−0.557 H/λ+0.335, and

when 0.55≦H/λ≦0.8, h/(λ·a)≦0.0667 (H/λ)²−0.11 H/λ+0.2103, andadditionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧1.133 (H/λ)²−1.043 H/λ+0.391,

when 0.45≦H/λ<0.6, h/(λ·a)≧0.133 (H/λ)²−0.183 H/λ+0.2065, and

when 0.6≦H/λ<0.8, h/(λ·a)≧−0.0075 H/λ+0.149.

As shown in FIG. 60, there are ranges where k² is equal to or smallerthan 0.00015, when 17.5°<θ<18.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦4 (H/λ)²−3.28 H/λ+0.848,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.467 (H/λ)²−0.537 H/λ+0.316, and

when 0.55≦H/λ≦0.8, h/(λ·a)≦0.1 (H/λ)²−0.155 H/λ+0.217, and additionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧0.867 (H/λ)²−0.817 H/λ+0.337,

when 0.45≦H/λ<0.55, h/(λ·a)≧−0.05 H/λ+0.1675, and

when 0.55≦H/λ≦0.8, h/(λ·a)≧−0.008 H/λ+0.1444.

As shown in FIG. 61, there are ranges where k² is equal to or smallerthan 0.00015, when 18.5°≦θ<19.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦2.8 (H/λ)²−2.34 H/λ+0.655,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.467 (H/λ)²−0.537 H/λ+0.307, and

when 0.55≦H/λ≦0.8, h/(λ·a)≦0.04 (H/λ)²−0.07 H/λ+0.1794, andadditionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧0.933 (H/λ)²−0.847 H/λ+0.331, and

when 0.45≦H/λ<0.6, h/(λ·a)≧0.081 (H/λ)²−0.118 H/λ+0.1759, and

when 0.6≦H/λ≦0.8, h/(λ·a)≧−0.005 H/λ+0.137.

As shown in FIG. 62, there are ranges where k² is equal to or smallerthan 0.00015, when 19.5°≦θ≦20.5° and

when 0.3≦H/λ<0.4, h/(λ·a)≦2.4 (H/λ)²−2 H/λ+0.574,

when 0.4≦H/λ<0.55, h/(λ·a)≦0.4 (H/λ)²−0.46 H/λ+0.278, and

when 0.55≦H/λ≦0.8, h/(λ·a)≦0.0933 (H/λ)²−0.142 H/λ+0.1959, andadditionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧0.667 (H/λ)²−0.627 H/λ+0.281, and

when 0.45≦H/λ<0.575, h/(λ·a)≧0.107 (H/λ)²−0.141 H/λ+0.176, and

when 0.575≦H/λ≦0.8, h/(λ·a)≧−0.00444 H/λ+0.1326.

As shown in FIG. 63, there are ranges where k² is equal to or smallerthan 0.00015, when 20.5°≦θ<21.5° and

when 0.3≦H/<0.4, h/(λ·a)≦2.2 (H/λ)²−1.83 H/λ+0.529,

when 0.4≦H/λ<0.52, h/(λ·a)≦0.357 (H/λ)²−0.404 H/λ+0.2533, and

when 0.52≦H/λ≦0.8, h/(λ·a)≦0.0604 (H/λ)²0.0976 H/λ+0.1744, andadditionally,

when 0.3≦H/λ<0.45, h/(λ·a)≧0.733 (H/λ)²−0.657 H/λ+0.276, and

when 0.45≦H/λ≦0.8, h/(λ·a)≧0.04286 (H/λ)²−0.065 H/λ+0.1496.

As shown in FIG. 64, there are ranges where k² is equal to or smallerthan 0.00015, when 21.5°≦θ<22.5° and

when 0.3≦H/λ≦0.8, h/(λ·a)≦0.198 (H/λ)²−0.291 H/λ+0.234, andadditionally,

when 0.3≦H/λ≦0.45, h/(λ·a)≧0.8 (H/λ)²−0.69 H/λ+0.2735, and

when 0.45≦H/λ≦0.8, h/(λ·a)²−0.00286 H/λ+0.1263.

As shown in FIG. 65, there are ranges where k² is equal to or smallerthan 0.00015, when 22.5°≦θ<23.5° and

when 0.3≦H/λ<0.7, h/(λ·a)≦0.568 (H/λ)²−0.649 H/λ+0.2976, and

when 0.7≦H/λ<0.75, h/(λ·a)≦−0.03 H/λ+0.1425, and additionally,

when 0.3≦H/λ<0.73, h/(λ·a)≧0.136 (H/λ)²−0.174 H/λ+0.1719, and

when 0.73≦H/λ≦0.75, h/(λ·a)≧0.125 H/λ+0.02625.

As shown in FIG. 66, there are ranges where k² is equal to or smallerthan 0.00015, when 23.5°≦θ<24° and

when 0.3≦H/λ<0.5, h/(λ·a)≦0.4 (H/λ)²−0.46 H/λ+0.246, and

when 0.5≦H/λ≦0.8, h/(λ·a)≦0.116, and additionally,

when 0.3≦H/λ<0.5, h/(λ·a)≧0.667 (H/λ)²−0.613 H/λ+0.253, and

when 0.5≦H/λ≦0.8, h/(λ·a)≧−0.01 H/λ+0.118.

when 23.5°≦θ≦24° and

when 0.3≦H/λ≦0.42, h/(λ·a)≦−0.208 H/λ+0.128, and additionally,

when 0.3≦H/λ≦0.42, h/(λ·a)≧−0.125 H/λ+0.0925.

As shown in FIG. 67, there is no range where k² is equal to or smallerthan 0.00015, when θ=177°.

Although a few specific exemplary embodiments employed in the presentinvention have been shown and described, it would be appreciated bythose skilled in the art that changes may be made in these exemplaryembodiments without departing from the principles and spirit of theinvention, the scope of which is defined in the claims and theirequivalents.

The present invention is based on Japanese Patent Application No.2006-053486 filed on Feb. 28, 2006 and Japanese Patent Application No.2007-017473 filed on Jan. 29, 2007, the entire disclosure of which ishereby incorporated by reference.

1. An elastic boundary wave device comprising: a LiNbO₃ substrate; anelectrode exciting an elastic wave and provided on the substrate; and asilicon oxide film provided on the substrate to cover the electrode,wherein parameters of the elastic boundary wave device have any one ofranges below, where “θ” is a rotation Y cut angle of the substrate, “a”is a ratio of copper density with respect to a density of a materialused as the electrode, “λ” is a wavelength of the elastic wave excitedby the electrode, “h” is a film thickness of the electrode, “H” is athickness of the silicon oxide film: when 0.045λ/a≦h<0.0525λ/a, and when25°≦θ<26.5°, 0.39λ≦H<0.46λ, when 26.5°≦θ<27.5°, 0.41λ≦H<0.48λ, when27.5°≦θ<28.5°, 0.42λ≦H<0.51λ, when 28.5°≦θ<29.5°, 0.43λ≦H<0.53λ, when29.5°≦θ<30.5°, 0.45λ≦H<0.56λ, when 30.5°≦θ<31.5°, 0.46λ≦H<0.58λ, when31.5°≦θ<32.5°, 0.47λ≦H<0.61λ, when 32.5°≦θ<33.5°, 0.48λ≦H<0.64λ, when33.5°≦θ<35°, 0.48λ≦H<0.67λ, when 35°≦θ<37.5°, 0.5λ≦H<0.74λ, when37.5°≦θ<42°, 0.52λ≦H<0.8λ, when 42°≦θ<57°, 0.55λ≦H<0.8λ, when 57°≦θ<63°,0.51λ≦H<0.8λ, when 63°≦θ<69°, 0.46λ≦H<0.8λ, when 69°≦θ<75°,0.39λ≦H<0.8λ, when 75°≦θ<99°, 0.3λ≦H<0.8λ, and when 99°≦θ<105°,0.58λ≦H<0.8λ, when 0.0525λ/a≦h<0.065λ/a and when 24°≦θ<25°,0.3λ≦H<0.32λ, when 25°≦θ<26.5°, 0.3λ≦H<0.37λ, when 26.5°≦θ<27.5°,0.33λ≦H<0.38λ, when 27.5°≦θ<28.5°, 0.34λ≦H<0.41λ, when 28.5°≦θ<29.5°,0.37λ≦H<0.43λ, when 29.5°≦θ<30.5°, 0.39λ≦H<0.44λ, when 30.5°≦θ<31.5°,0.42λ≦H<0.47λ, when 31.5°≦θ<32.5°, 0.44λ≦H<0.48λ, when 32.5°≦θ<33.5°,0.47λ≦H<0.49λ, when 33.5°≦θ<34.5°, 0.47λ≦H<0.51λ, when 34.5°≦θ<35.5°,0.48λ≦H<0.57λ, when 35.5°≦θ<36.5°, 0.5λ≦H<0.62λ, when 36.5°≦θ<38°,0.52λ≦H<0.67λ, when 38°≦θ<40.5°, 0.54λ≦H<0.79λ, when 40.5°≦θ<43.5°,0.58λ≦H<0.8λ, when 43.5°≦θ<46.5°, 0.61λ≦H<0.8λ, when 46.5°≦θ<51°,0.64λ≦H<0.8λ, when 51°≦θ<57°, 0.69λ≦H<0.8λ, and when 57°≦θ<63°,0.78λ≦H<0.8λ, when 0.065λ/a≦h<0.0725λ/a and when 25.5°≦θ<26.5°,0.3λ≦H<0.32λ, when 26.5°≦θ<27.5°, 0.3λ≦H<0.36λ, when 27.5°≦θ<28.5°,0.3λ≦H<0.38λ, when 28.5°≦θ<29.5°, 0.32λ≦H<0.43λ, when 29.5°≦θ<30.5°,0.34λ≦H<0.46λ, when 30.5°≦θ<31.5°, 0.36λ≦H<0.5λ, when 31.5°≦θ<32.5°,0.39λ≦H<0.55λ, when 32.5°≦θ<33.5°, 0.43λ≦H<0.6λ, when 33.5°≦θ<35°,0.46λ≦H<0.66λ, when 35°≦θ<36.5°, 0.54λ≦H<0.8λ, when 36.5°≦θ<37.5°,0.59λ≦H<0.8λ, when 37.5°≦θ<38.5°, 0.65λ≦H<0.8λ, and when 38.5°≦θ<39°,0.73λ≦H<0.8λ, when 0.0725λ/a≦h<0.0775λ/a and when 26.5°≦θ<27.5°,0.3λ≦H<0.35λ, when 27.5°≦θ<28.5°, 0.3 λ≦H<0.39λ, when 28.5°≦θ<29.5°,0.3λ≦H<0.43λ, when 29.5°≦θ<30.5°, 0.33λ≦H<0.49λ, when 30.5°≦θ<31.5°,0.35λ≦H<0.56λ, when 31.5°≦θ<32.5°, 0.39λ≦H<0.63λ, when 32.5°≦θ<33.5°,0.43λ≦H<0.75λ, when 33.5°≦θ<34.5°, 0.47λ≦H<0.8λ, when 34.5°≦θ<35.5°,0.52λ≦H<0.8λ, when 35.5°≦θ<36.5°, 0.57λ≦H<0.8λ, when 36.5°≦θ≦37.5°,0.63λ≦H<0.8λ, and when 37.5°≦θ<38.5°, 0.72λ≦H<0.8λ, when0.0775λ/a≦h<0.0825λ/a and when 26.5°≦θ<27.5°, 0.3λ≦H<0.34λ, when27.5°≦θ<28.5°, 0.3λ≦H<0.41λ, when 28.5°≦θ<29.5°, 0.3λ≦H<0.47λ, when29.5°≦θ<30.5°, 0.32λ≦H<0.56λ, when 30.5°≦θ<31.5°, 0.36λ≦H<0.69λ, when31.5°≦θ<32.5°, 0.39λ≦H<0.8λ, when 32.5°≦θ<33.5°, 0.44λ≦H<0.8λ, when33.5°≦θ<35°, 0.5λ≦H<0.8λ, when 35°≦θ<36.5°, 0.65λ≦H<0.8λ, and when36.5°≦θ<38°, 0.77λ≦H<0.8λ, when 0.0825λ/a≦h<0.0875λ/a and when26.5°≦θ<27.5°, 0.3λ≦H<0.36λ, when 27.5°≦θ<28.5°, 0.3λ≦H<0.44λ, when28.5°≦θ<29.5°, 0.3λ≦H<0.57λ, when 29.5°≦θ<30.5°, 0.32λ≦H<0.8λ, when30.5°≦θ<31.5°, 0.37λ≦H<0.8λ, when 31.5°≦θ<32.5°, 0.43λ≦H<0.8λ, when32.5°≦θ<33.5°, 0.51λ≦H<0.8λ, when 33.5°≦θ<34.5°, 0.59λ≦H<0.8λ, and when34.5°≦θ<35.5°, 0.72λ≦H<0.8 λ. when 0.0875λ/a≦h<0.0925λ/a and when26.5°≦θ<27.5°, 0.3λ≦H<0.39λ, when 27.5°≦θ<28.5°, 0.3λ≦H<0.58λ, when28.5°≦θ<29.5°, 0.3λ≦H<0.8λ, when 29.5°≦θ<30.5°, 0.33λ≦H<0.8λ, when30.5°≦θ<31.5°, 0.43λ≦H<0.8λ, when 31.5°≦θ<32.5°, 0.53λ≦H<0.8λ, and when32.5°≦θ<33.5°, 0.67λ≦H<0.8λ, when 0.0925λ/a≦h<0.0975λ/a and when26.5°≦θ<27.5°, 0.3λ≦H<0.63λ, when 27.5°≦θ<28.5°, 0.3λ≦H<0.8λ, when28.5°≦θ<29.5°, 0.3λ≦H<0.8λ, when 29.5°≦θ<30.5°, 0.42λ≦H<0.8λ, and when30.5°≦θ<31.5°, 0.6λ≦H<0.8λ, when 0.0975λ/a≦h<0.1025λ/a and when25.5°≦θ<26.5°, 0.32λ≦H<0.7λ, when 26.5°≦θ<27.5°, 0.3λ≦H<0.8λ, when27.5°≦θ<28.5°, 0.3λ≦H<0.8λ, and when 28.5°≦θ<29.5°, 0.45λ≦H<0.8λ, when0.1025λ/a≦h<0.1125λ/a and when 24.5°≦θ<25.5°, 0.6λ≦H<0.8λ, when25.5°≦θ<26.5°, 0.3λ≦H<0.8λ, when 26.5°≦θ<27.5°, 0.3λ≦H<0.8λ, and when27.5°≦θ<28.5°, 0.3λ≦H<0.33λ and 0.64λ≦H<0.8λ, and when0.1125λ/a≦h<0.12λ/a and when 22.5°≦θ<23.5°, 0.47λ≦H<0.76λ, and when23.5°≦θ<24.5°, 0.36λ≦H<0.45 λ.
 2. An elastic boundary wave devicecomprising: a LiNbO₃ substrate; an electrode exciting an elastic waveand provided on the substrate; and a silicon oxide film provided on thesubstrate to cover the electrode, wherein parameters of the elasticboundary wave device have any one of ranges below, where “θ” is arotation Y cut angle of the substrate, “a” is a ratio of copper densitywith respect to a density of a material used as the electrode, “λ” is awavelength of the elastic wave excited by the electrode, “h” is a filmthickness of the electrode, “H” is a thickness of the silicon oxidefilm: when 0°≦θ<0.5° and when 0.6≦H/λ<0.8, h/(λ·a)≦H/λ, andadditionally, when 0.6≦H/λ<0.625, h/(λ·a)≧−2 H/λ+1.8, and when0.625≦H/λ≦0.8, h/(λ·a)≧1.543 (H/λ)²−2.484 H/λ+1.5, when 0.5°≦θ<2° andwhen 0.508≦H/λ≦0.8, h/(λ·a)≦H/λ, and additionally, when 0.508≦H/λ<0.531,h/(λ·a)≧−0.3478 H/λ+0.6847, when 0.531≦H/λ<0.6, h/(λ·a)≧−0.6087H/λ+0.8232, and when 0.6≦H/λ≦0.8, h/(λ·a)≧0.6 (H/λ)²−0.98 H/λ+0.83, when2°≦θ<4.5° and when 0.45≦H/λ<0.8, h/(λ·a)≦H/λ, and additionally, when0.45≦H/λ<0.5, h/(λ·a)≧28.998 (H/λ)²−29.088 H/λ+7.668, when 0.5≦H/λ<0.65,h/(λ·a)≧1.6 (H/λ)²−2.06 H/λ+1.003, and when 0.65≦H/λ≦0.8,h/(λ·a)≧−0.0733 H/λ+0.3877, when 4.5°≦θ<7.5° and when 0.3625≦H/λ<0.496,h/(λ·a)≦H/λ, when 0.496≦H/λ<0.55, h/(λ·a)≦−0.111 H/λ+0.5511, when0.55≦H/λ<0.65, h/(λ·a)≦3.4 (H/λ)²−4.45 H/λ+1.909, when 0.65≦H/λ<0.7,h/(λ·a)≦−0.06 H/λ+0.492, and when 0.7≦H/λ≦0.8, h/(λ·a)≦0.45, andadditionally, when 0.3625≦H/λ<0.3875, h/(λ·a)≧−0.46 H/λ+0.5293, when0.3875≦H/λ<0.4, h/(λ·a)≧−2.96 H/λ+1.498, when 0.4≦H/λ<0.45,h/(λ·a)≧−0.58 H/λ+0.546, when 0.45≦H/λ<0.6, h/(λ·a)≧1.2667 (H/λ)²−1.503H/λ+0.705, and when 0.6≦H/λ≦0.8, h/(λ·a)≧−0.04 H/λ+0.283, when7.5°≦θ<9.5° and when 0.315≦H/λ<0.406, h/(λ·a)≦H/λ, when 0.406≦H/λ<0.419,h/(λ·a)≦−1.077 H/λ+0.8432, when 0.419≦H/λ<0.45, h/(λ·a)≦61.7512(H/λ)²−55.565 H/λ+12.8326, when 0.45≦H/λ<0.6, h/(λ·a)≦1.8667(H/λ)²−2.233 H/λ+0.96, and when 0.6≦H/λ≦0.8, h/(λ·a)≦0.2 (H/λ)²−0.32H/λ+0.412, and additionally, when 0.315≦H/λ<0.342, h/(λ·a)≧−0.5556H/λ+0.49, when 0.342≦H/λ<0.35, h/(λ·a)≧−3.75 H/λ+1.5825, when0.35≦H/λ<0.4, h/(λ·a)≧−0.6 H/λ+0.48, when 0.4≦H/λ<0.55, h/(λ·a)≧1.133(H/λ)²−1.243 H/λ+0.556, and when 0.55≦H/λ≦0.8, h/(λ·a)≧0.1067(H/λ)²−0.18 H/λ+0.2817, when 9.5°≦θ<10.5° and when 0.31≦H/λ<0.37,h/(λ·a)≦H/λ, when 0.37≦H/λ<0.383, h/(λ·a)≦0.37, when 0.383≦H/λ<0.392,h/(λ·a)≦−1.111 H/λ+0.7956, when 0.392≦H/λ<0.4, h/(λ·a)≦−2.5 H/λ+1.34,when 0.4≦H/λ<0.45, h/(λ·a)≦12 (H/λ)²−11.1 H/λ+2.86, when 0.45≦H/λ<0.5,h/(λ·a)≦3.2 (H/λ)²−3.36 H/λ+1.159, when 0.5≦H/λ<0.61, h/(λ·a)≦0.5455(H/λ)²−0.7327 H/λ+0.509, and when 0.61≦H/λ≦0.8, h/(λ·a)≦0.08848(H/λ)²−0.1616 H/λ+0.3307, and additionally, when 0.31≦H/λ<0.331,h/(λ·a)≧−0.4762 H/λ+0.4576, when 0.331≦H/λ<0.35, h/(λ·a)≧−2.632H/λ+1.171, when 0.35≦H/λ<0.4, h/(λ·a)≧−0.5 H/λ+0.425, when 0.4≦H/λ<0.5,h/(λ·a)≧(H/λ)²−1.09H/λ+0.501, and when 0.5≦H/λ≦0.8, h/(λ·a)≧0.1(H/λ)²−0.17 H/λ+0.266, when 10.5°≦θ<11.5° and when 0.304≦H/λ<0.36,h/(λ·a)≦H/λ, when 0.36≦H/λ<0.3625, h/(λ·a)≦−4 H/λ+1.8, when0.3625≦H/λ<0.375, h/(λ·a)≦−0.8 H/λ+0.64, when 0.375≦H/λ<0.4,h/(λ·a)≦80.702 (H/λ)²−64.344 H/λ+13.120, when 0.4≦H/λ<0.5, h/(λ·a)≦3(H/λ)²−3.091 H/λ+1.051, when 0.5≦H/λ<0.7, h/(λ·a)≦0.4 (H/λ)²−0.56H/λ+0.436, and when 0.7≦H/λ≦0.8, h/(λ·a)≦−0.02 H/λ+0.254, andadditionally, when 0.304≦H/λ<0.329, h/(λ·a)≧−0.56 H/λ+0.474, when0.329≦H/λ<0.331, h/(λ·a)≧−15 H/λ+5.225, when 0.331≦H/λ<0.35,h/(λ·a)≧−1.579 H/λ+0.7826, when 0.35≦H/λ<0.4, h/(λ·a)≧−0.4 H/λ+0.37,when 0.4≦H/λ<0.575, h/(λ·a)≧0.4762 (H/λ)²−0.5786 H/λ+0.3652, and when0.575≦H/λ≦0.8, h/(λ·a)≧0.0381 (H/λ)²−0.07905 H/λ+0.2229, when11.5°≦θ<12.5°, and when 0.3≦H/λ<0.35, h/(λ·a)≦H/λ, when 0.35≦H/λ<0.358,h/(λ·a)≦−1.25 H/λ+0.7875, when 0.358≦H/λ<0.3625, h/(λ·a)≦−6.667H/λ+2.7267, when 0.3625≦H/λ<0.4, h/(λ·a)≦27.781 (H/λ)²−22.3379H/λ+4.7569, when 0.4≦H/λ<0.5, h/(λ·a)≦2.18 (H/λ)²−2.271 H/λ+0.8263, when0.5≦H/λ<0.65, h/(λ·a)≦0.44 (H/λ)²−0.578 H/λ+0.4148, and when0.65≦H/λ<0.8, h/(λ·a)≦−0.02667 H/λ+0.2423, and additionally, when0.3≦H/λ<0.308, h/(λ·a)≧−0.5 H/λ+0.45, when 0.308≦H/λ<0.35,h/(λ·a)≧25.1541 (H/λ)²−18.099 H/λ+3.4683, when 0.35≦H/λ<0.45,h/(λ·a)≧1.8 (H/λ)²−1.69 H/λ+0.586, when 0.45≦H/λ<0.6, h/(λ·a)≧0.3333(H/λ)²−0.4167 H/λ+0.31, and when 0.6≦H/λ≦0.8, h/(λ·a)≧−0.02 H/λ+0.192,when 12.5°≦θ<13.5° and when 0.3≦H/λ<0.32, h/(λ·a)≦H/λ, when0.32≦H/λ<0.35, h/(λ·a)≦−H/λ+0.64, when 0.35≦H/λ<0.373, h/(λ·a)≦−1.3044H/λ+0.7465, when 0.373≦H/λ<0.4, h/(λ·a)≦−0.6296 H/λ+0.4949, when0.4≦H/λ<0.5, h/(λ·a)≦1.6 (H/λ)²−1.66 H/λ+0.651, when 0.5≦H/λ<0.65,h/(λ·a)≦0.4667 (H/λ)²−0.61 H/λ+0.4093, and when 0.65≦H/λ≦0.8,h/(λ·a)≦−0.02 H/λ+0.223, and additionally, when 0.3≦H/λ<0.35,h/(λ·a)≧−0.8 H/λ+0.48, when 0.35≦H/λ<0.45, h/(λ·a)≧−0.2 H/λ+0.27, when0.45≦H/λ<0.625, h/(λ·a)≧0.09524 (H/λ)²−0.1595 H/λ+0.2325, and when0.65≦H/λ≦0.8, h/(λ·a)≧−0.01143 H/λ+0.1771, when 13.5°≦θ<14.5° and when0.3≦H/λ<0.318, h/(λ·a)≦H/λ, when 0.318≦H/λ<0.325, h/(λ·a)≦−4 H/λ+1.59,when 0.325≦H/λ<0.4, h/(λ·a)≦6.933 (H/λ)²−5.88 H/λ+1.4687, when0.4≦H/λ<0.585, h/(λ·a)≦0.6618 (H/λ)²−0.7924 H/λ+0.437, and when0.585≦H/λ≦0.8, h/(λ·a)≦0.11527 (H/λ)²−0.1829 H/λ+0.2676, andadditionally, when 0.3≦H/λ<0.35, h/(λ·a)≧−0.6 H/λ+0.4, when0.35≦H/λ<0.475, h/(λ·a)≧0.8 (H/λ)²−0.82 H/λ+0.379, when 0.475≦H/λ<0.65,h/(λ·a)≧0.2095 (H/λ)²−0.2814 H/λ+0.2564, and when 0.65≦H/λ≦0.8,h/(λ·a)≧−0.0133 H/λ+0.1707, when 14.5°≦θ<15.5° and when 0.3≦H/λ<0.304,h/(λ·a)≦H/λ, when 0.304≦H/λ<0.308, h/(λ·a)≦−1.25 H/λ+0.685, when0.308≦H/λ<0.321, h/(λ·a)≦−2.308 H/λ+1.011, when 0.321≦H/λ<0.375,h/(λ·a)≦11.239 (H/λ)²−8.748 H/λ+1.920, when 0.375≦H/λ<0.5,h/(λ·a)≦1.1733 (H/λ)²−1.2347 H/λ+0.518, when 0.5≦H/λ<0.65, h/(λ·a)≦0.267(H/λ)²−0.36 H/λ+0.3073, and when 0.65≦H/λ≦0.8, h/(λ·a)≦−0.01333H/λ+0.1947, and additionally, when 0.3≦H/λ<0.35, h/(λ·a)≧−0.5 H/λ+0.355,when 0.35≦H/λ<0.4, h/(λ·a)≧−0.2 H/λ+0.25, when 0.4≦H/λ<0.5, h/(λ·a)≧−0.1H/λ+0.21, when 0.5≦H/λ<0.7, h/(λ·a)≧−0.03 H/λ+0.175, and when0.7≦H/λ≦0.8, h/(λ·a)≧0.154, when 15.5°≦θ<16.5° and when 0.3≦H/λ<0.308,h/(λ·a)≦−1.25 H/λ+0.675, when 0.308≦H/λ<0.311, h/(λ·a)≦−10 H/λ+3.37,when 0.311≦H/λ<0.321, h/(λ·a)≦−2 H/λ+0.882, when 0.321≦H/λ<0.4,h/(λ·a)≦5.9188 (H/λ)²−4.799 H/λ+1.171, when 0.4≦H/λ<0.55, h/(λ·a)≦0.711(H/λ)²−0.7956 H/λ+0.4024, when 0.55≦H/λ≦0.8, h/(λ·a)≦0.128 (H/λ)²−0.197H/λ+0.2495, and additionally, when 0.3≦H/λ<0.35, h/(λ·a)≧−0.4 H/λ+0.31,when 0.35≦H/λ<0.5, h/(λ·a)≧0.3556 (H/λ)²−0.4089 H/λ+0.2696, and when0.5≦H/λ≦0.8, h/(λ·a)≧0.08762 (H/λ)²−0.1306 H/λ+0.1974, when16.5°≦θ<17.5° and when 0.3≦H/λ<0.4, h/(λ·a)≦8.6 (H/λ)²−6.75 H/λ+1.511,when 0.4≦H/λ<0.55, h/(λ·a)≦0.467 (H/λ)²−0.557 H/λ+0.335, and when0.55≦H/λ≦0.8, h/(λ·a)≦0.0667 (H/λ)²−0.11 H/λ+0.2103, and additionally,when 0.3≦H/λ<0.45, h/(λ·a)≧1.133 (H/λ)²−1.043 H/λ+0.391, when0.45≦H/λ<0.6, h/(λ·a)≧0.133 (H/λ)²−0.183 H/λ+0.2065, and when0.6≦H/λ≦0.8, h/(λ·a)≧−0.0075 H/λ+0.149, when 17.5°≦θ<18.5° and when0.3≦H/λ<0.4, h/(λ·a)≦4 (H/λ)²−3.28 H/λ+0.848, when 0.4≦H/λ<0.55,h/(λ·a)≦0.467 (H/λ)²−0.537 H/λ+0.316, and when 0.55≦H/λ≦0.8, h/(λ·a)≦0.1(H/λ)²−0.155 H/λ+0.217, and additionally, when 0.3≦H/λ<0.45,h/(λ·a)≧0.867 (H/λ)²−0.817 H/λ+0.337, when 0.45≦H/λ<0.55, h/(λ·a)≧−0.05H/λ+0.1675, and when 0.55≦H/λ≦0.8, h/(λ·a)≧0.008 H/λ+0.1444, when18.5°≦θ<19.5° and when 0.3≦H/λ<0.4, h/(λ·a)≦2.8 (H/λ)²−2.34 H/λ+0.655,when 0.4≦H/λ<0.55, h/(λ·a)≦0.467 (H/λ)²−0.537 H/λ+0.307, and when0.55≦H/λ≦0.8, h/(λ·a)≦0.04 (H/λ)²−0.07 H/λ+0.1794, and additionally,when 0.3≦H/λ<0.45, h/(λ·a)≧0.933 (H/λ)²−0.847 H/λ+0.331, and when0.45≦H/λ<0.6, h/(λ·a)≧0.081 (H/λ)²−0.118 H/λ+0.1759, and when0.6≦H/λ≦0.8, h/(λ·a)≧−0.005 H/λ+0.137, when 19.5°≦θ<20.5° and when0.3≦H/λ<0.4, h/(λ·a)≦2.4 (H/λ)²−2 H/λ+0.574, when 0.4≦H/λ<0.55,h/(λ·a)≦0.4 (H/λ)²−0.46 H/λ+0.278, and when 0.55≦H/λ≦0.8, h/(λ·a)≦0.0933(H/λ)²−0.142 H/λ+0.1959, and additionally, when 0.3≦H/λ<0.45,h/(λ·a)≧0.667 (H/λ)²−0.627 H/λ+0.281, and when 0.45≦H/λ<0.575,h/(λ·a)≧0.107 (H/λ)²−0.141 H/λ+0.176, and when 0.575≦H/λ≦0.8,h/(λ·a)≧−0.00444 H/λ+0.1326, when 20.5°≦θ<21.5° and when 0.3≦H/λ<0.4,h/(λ·a)≦2.2 (H/λ)²−1.83 H/λ+0.529, when 0.4≦H/λ<0.52, h/(λ·a)≦0.357(H/λ)²−0.404 H/λ+0.2533, and when 0.52≦H/λ≦0.8, h/(λ·a)≦0.0604(H/λ)²−0.0976 H/λ+0.1744, and additionally, when 0.3≦H/λ<0.45,h/(λ·a)≧0.733 (H/λ)²−0.657 H/λ+0.276, and when 0.45≦H/λ≦0.8,h/(λ·a)≧0.04286 (H/λ)²−0.065 H/λ+0.1496, when 21.5°≦θ<22.5° and when0.3≦H/λ≦0.8, h/(λ·a)≦0.198 (H/λ)²−0.291 H/λ+0.234, and additionally,when 0.3≦H/λ<0.45, h/(λ·a)≧0.8 (H/λ)²−0.69 H/λ+0.2735, and when0.45≦H/λ≦0.8, h/(λ·a)≧−0.00286 H/λ+0.1263, when 22.5°≦θ<23.5° and when0.3≦H/λ<0.7, h/(λ·a)≦0.568 (H/λ)²−0.649 H/λ+0.2976, and when0.7≦H/λ<0.75, h/(λ·a)≦−0.03 H/λ+0.1425, and additionally, when0.3≦H/λ<0.73, h/(λ·a)≧0.136 (H/λ)²−0.174 H/λ+0.1719, and when0.73≦H/λ<0.75, h/(λ·a)≧0.125 H/λ+0.02625, when 23.5°≦θ<24° and when0.3≦H/λ<0.5, h/(λ·a)≦0.4 (H/λ)²−0.46 H/λ+0.246, and when 0.5≦H/λ≦0.8,h/(λ·a)≦0.116, and additionally, when 0.3≦H/λ<0.5, h/(λ·a)≧0.667(H/λ)²−0.613 H/λ+0.253, and when 0.5≦H/λ≦0.8, h/(λ·a)≧−0.01 H/λ+0.118,or when 23.5°≦θ<24° and when 0.3≦H/λ<0.42, h/(λ·a)≦−0.208 H/λ+0.128, andadditionally, when 0.3≦H/λ<0.42, h/(λ·a)≧−0.125 H/λ+0.0925.
 3. Anelastic boundary wave device comprising: a LiNbO₃ substrate; anelectrode exciting an elastic wave and provided on the substrate; and asilicon oxide film provided on the substrate to cover the electrode,wherein parameters of the elastic boundary wave device have any one ofranges below, where “θ” is a rotation Y cut angle of the substrate, “a”is a ratio of copper density with respect to a density of a materialused as the electrode, “λ” is a wavelength of the elastic wave excitedby the electrode, “h” is a film thickness of the electrode, “H” is athickness of the silicon oxide film: when 0.03λ/a≦h<0.0375λ/a and when0.3≦H/λ≦0.8, θ≦75 (H/λ)²−82.5 H/λ+103.687, and additionally, when0.3≦H/λ<0.65, θ≧−85.7 H/λ+97.7, and when 0.65≦H/λ≦0.8, θ≧42, or when0.03λ/a≦h<0.0375λ/a and when 0.45≦H/λ<0.65, θ≦120H/λ−36, and when0.65≦H/λ≦0.8, θ≦42, and additionally, when 0.45≦H/λ<0.5, θ≧18, and when0.5≦H/λ≦0.8, θ≧40 H/λ−2, when 0.0375λ/a≦h<0.0525λ/a and when0.3≦H/λ≦0.8, θ≦24 H/λ+88.8, and additionally, when 0.3≦H/λ<0.55, θ≧−120H/λ+114, and when 0.55≦H/λ≦0.8, θ≧48, or when 0.0375λ/a≦h<0.0525λ/a andwhen 0.43≦H/λ<0.55, θ≦180 H/80 −51, and when 0.55≦H/λ≦0.8, θ≦48, andadditionally, when 0.43≦H/λ≦0.8, θ≧34.3 H/λ+11.6, when0.0525λ/a≦h<0.065λ/a and when 0.45≦H/λ≦0.8, θ≦80 H/λ−4, andadditionally, when 0.45≦H/λ≦0.8, θ≧20 H/λ+23, when 0.065λ/a≦h<0.0725λ/aand when 0.3≦H/λ<0.7, θ≦−26.7 (H/λ)²+52 H/λ+15.5, and when 0.7≦H/λ≦0.8,θ≦25 H/λ+21, and additionally, when 0.3≦H/λ≦0.8, θ≧−16.7 (H/λ)²+38.3H/λ+16, when 0.0725λ/a≦h<0.0775λ/a and when 0.3≦H/λ≦0.8, θ≦−25(H/λ)²+47.5 H/λ+17, and additionally, when 0.3≦H/λ≦0.8, θ≧−25(H/λ)²+42.5 H/λ+15.2, when 0.0775λ/a≦h<0.0825λ/a and when 0.3≦H/λ≦0.8,θ≦−21.4 (H/λ)²+38.2 H/λ+20.1, and additionally, when 0.3≦H/λ≦0.8,θ≧−23.3 (H/λ)²+35.8 H/λ+17.4, when 0.0825λ/a≦h<0.0875λ/a and when0.3≦H/λ≦0.8, θ≦−13.3 (H/λ)²+24.7 H/λ+24, and additionally, when0.3≦H/λ≦0.8, θ≧−16 (H/λ)²+25.6 H/λ+19.8, when 0.0875λ/a≦h<0.0925λ/a, andwhen 0.3≦H/λ<0.55, θ≦10 H/λ+26.5, and when 0.55≦H/λ≦0.8, θ≦6 H/λ+28.7,and additionally, when 0.3≦H/λ≦0.8, θ≧4 H/λ+25.3, when0.0925λ/a≦h<0.0975λ/a and when 0.3≦H/λ≦0.8, θ≦4 H/λ+28.3, andadditionally, when 0.3≦H/λ≦0.8, θ≧2 H/λ+25.9, when 0.0975λ/a≦h<0.1025λ/aand when 0.3<H/λ≦0.8, θ≦2 H/λ+28.2, and additionally, when 0.3≦H/λ≦0.8,θ≧26, and when 0.1025λ/a≦h<0.105λ/a and when 0.3≦H/λ≦0.8, θ≦28, andadditionally, when 0.3≦H/λ<0.5, θ≧−5 H/λ+27.5, and when 0.5≦H/λ≦0.8,θ≧25.
 4. The elastic boundary wave device as claimed in claim 2, whereina propagation direction of the elastic wave having a main component ofSH wave is an x-axis direction of the substrate.
 5. The elastic boundarywave device as claimed in claim 2, further comprising a medium membraneprovided on the silicon oxide film.
 6. The elastic boundary wave deviceas claimed in claim 5, wherein a sound velocity in the medium membraneis faster than that in the silicon oxide film.
 7. The elastic boundarywave device as claimed in claim 5, wherein the medium membrane includesany of silicon nitride, aluminum silicon, aluminum oxide, and silicon.8. The elastic boundary wave device as claimed in claim 2, wherein thedensity of the electrode is greater than that of the silicon oxide film.9. The elastic boundary wave device as claimed in claim 2, wherein theelectrode includes copper.
 10. The elastic boundary wave device asclaimed in claim 2, wherein the electrode has a multilayer structurewith two or more layers.
 11. The elastic boundary wave device as claimedin claim 10, wherein the electrode includes a titanium layer provided onthe substrate and a copper layer provided on the titanium layer.
 12. Theelastic boundary wave device as claimed in claim 2, further comprising abarrier layer covering the electrode.
 13. A resonator comprising theelastic boundary wave device as claimed in any one of claims 1 through3.
 14. A filter comprising the elastic boundary wave device as claimedin any one of claims 1 through 3.